 4.1: In Exercises 1 and 2, draw the graph of the inverse of the given fu...
 4.4.1.1: In Exercises 1 to 4, assume that the given function has an inverse ...
 4.4.5.1: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.1: In Exercises 1 to 8, evaluate the exponential function for the give...
 4.4.3.1: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.1: Population Growth In Exercises 1 to 6, solve the givenproblem relat...
 4.4.7.1: In Exercises 1 to 6, use a scatter plot of the given data to determ...
 4.4.4.1: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.2: In Exercises 1 and 2, draw the graph of the inverse of the given fu...
 4.4.1.2: In Exercises 1 to 4, assume that the given function has an inverse ...
 4.4.5.2: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.2: In Exercises 1 to 8, evaluate the exponential function for the give...
 4.4.3.2: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.2: Population Growth In Exercises 1 to 6, solve the givenproblem relat...
 4.4.7.2: In Exercises 1 to 6, use a scatter plot of the given data to determ...
 4.4.4.2: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.3: In Exercises 3 to 6, use composition of functions to determine whet...
 4.4.1.3: In Exercises 1 to 4, assume that the given function has an inverse ...
 4.4.5.3: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.3: In Exercises 1 to 8, evaluate the exponential function for the give...
 4.4.3.3: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.3: Population Growth In Exercises 1 to 6, solve the givenproblem relat...
 4.4.7.3: In Exercises 1 to 6, use a scatter plot of the given data to determ...
 4.4.4.3: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.4: In Exercises 3 to 6, use composition of functions to determine whet...
 4.4.1.4: In Exercises 1 to 4, assume that the given function has an inverse ...
 4.4.5.4: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.4: In Exercises 1 to 8, evaluate the exponential function for the give...
 4.4.3.4: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.4: Population Growth In Exercises 1 to 6, solve the givenproblem relat...
 4.4.7.4: In Exercises 1 to 6, use a scatter plot of the given data to determ...
 4.4.4.4: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.5: In Exercises 3 to 6, use composition of functions to determine whet...
 4.4.1.5: If 3 is in the domain of f 1 find f f 1(3)4.
 4.4.5.5: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.5: In Exercises 1 to 8, evaluate the exponential function for the give...
 4.4.3.5: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.5: Population Growth In Exercises 1 to 6, solve the givenproblem relat...
 4.4.7.5: In Exercises 1 to 6, use a scatter plot of the given data to determ...
 4.4.4.5: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.6: In Exercises 3 to 6, use composition of functions to determine whet...
 4.4.1.6: If f is a onetoone function and f(0) = 5, f(1) = 2, and f(2) = 7 ...
 4.4.5.6: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.6: In Exercises 1 to 8, evaluate the exponential function for the give...
 4.4.3.6: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.6: Population Growth In Exercises 1 to 6, solve the givenproblem relat...
 4.4.7.6: In Exercises 1 to 6, use a scatter plot of the given data to determ...
 4.4.4.6: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.7: In Exercises 7 to 10, find the inverse of the function. Sketch the ...
 4.4.1.7: The domain of the inverse function is the of f1 is the ______ of f.
 4.4.5.7: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.7: In Exercises 1 to 8, evaluate the exponential function for the give...
 4.4.3.7: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.7: Medicine Sodium24 is a radioactive isotope of sodium that is used ...
 4.4.7.7: In Exercises 7 to 10, find the exponential regression function for ...
 4.4.4.7: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.8: In Exercises 7 to 10, find the inverse of the function. Sketch the ...
 4.4.1.8: The range of the inverse function f1 is the ________of f.
 4.4.5.8: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.8: In Exercises 1 to 8, evaluate the exponential function for the give...
 4.4.3.8: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.8: In Exercises 8 to 12, use the halflife information from Table 4.11...
 4.4.7.8: In Exercises 7 to 10, find the exponential regression function for ...
 4.4.4.8: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.9: In Exercises 7 to 10, find the inverse of the function. Sketch the ...
 4.4.1.9: In Exercises 9 to 16, draw the graph of the inverse relation. Is th...
 4.4.5.9: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.9: In Exercises 9 to 14, use a calculator to evaluate the exponential ...
 4.4.3.9: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.9: In Exercises 8 to 12, use the halflife information from Table 4.11...
 4.4.7.9: In Exercises 7 to 10, find the exponential regression function for ...
 4.4.4.9: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.10: In Exercises 7 to 10, find the inverse of the function. Sketch the ...
 4.4.1.10: In Exercises 9 to 16, draw the graph of the inverse relation. Is th...
 4.4.5.10: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.10: In Exercises 9 to 14, use a calculator to evaluate the exponential ...
 4.4.3.10: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.10: In Exercises 8 to 12, use the halflife information from Table 4.11...
 4.4.7.10: In Exercises 7 to 10, find the exponential regression function for ...
 4.4.4.10: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.11: In Exercises 11 and 12, find the inverse of the given function. f(x...
 4.4.1.11: In Exercises 9 to 16, draw the graph of the inverse relation. Is th...
 4.4.5.11: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.11: In Exercises 9 to 14, use a calculator to evaluate the exponential ...
 4.4.3.11: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.11: In Exercises 8 to 12, use the halflife information from Table 4.11...
 4.4.7.11: In Exercises 11 to 14, find the logarithmic regression function for...
 4.4.4.11: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.4.4.12: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.12: In Exercises 11 and 12, find the inverse of the given function. g(x...
 4.4.1.12: In Exercises 9 to 16, draw the graph of the inverse relation. Is th...
 4.4.5.12: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.12: In Exercises 9 to 14, use a calculator to evaluate the exponential ...
 4.4.3.12: In Exercises 1 to 12, write each equation in its exponential form. ...
 4.4.6.12: In Exercises 8 to 12, use the halflife information from Table 4.11...
 4.4.7.12: In Exercises 11 to 14, find the logarithmic regression function for...
 4.4.4.13: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.13: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.13: In Exercises 9 to 16, draw the graph of the inverse relation. Is th...
 4.4.5.13: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.13: In Exercises 9 to 14, use a calculator to evaluate the exponential ...
 4.4.3.13: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.13: Compound Interest In Exercises 13 to 20, solve the given problem re...
 4.4.7.13: In Exercises 11 to 14, find the logarithmic regression function for...
 4.4.4.14: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.14: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.14: In Exercises 9 to 16, draw the graph of the inverse relation. Is th...
 4.4.5.14: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.14: In Exercises 9 to 14, use a calculator to evaluate the exponential ...
 4.4.3.14: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.14: Compound Interest In Exercises 13 to 20, solve the given problem re...
 4.4.7.14: In Exercises 11 to 14, find the logarithmic regression function for...
 4.4.4.15: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.15: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.15: In Exercises 9 to 16, draw the graph of the inverse relation. Is th...
 4.4.5.15: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.15: In Exercises 15 and 16, examine the four functions and the graphs l...
 4.4.3.15: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.15: Compound Interest In Exercises 13 to 20, solve the given problem re...
 4.4.7.15: In Exercises 15 to 18, find the logistic regression function for th...
 4.4.4.16: In Exercises 1 to 16, expand the given logarithmic expression. Assu...
 4.16: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.16: In Exercises 9 to 16, draw the graph of the inverse relation. Is th...
 4.4.5.16: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.16: In Exercises 15 and 16, examine the four functions and the graphs l...
 4.4.3.16: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.16: Compound Interest In Exercises 13 to 20, solve the given problem re...
 4.4.7.16: In Exercises 15 to 18, find the logistic regression function for th...
 4.4.4.17: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.17: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.17: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.17: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.17: In Exercises 17 to 24, sketch the graph of each function. f(x) = 3x
 4.4.3.17: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.17: Compound Interest In Exercises 13 to 20, solve the given problem re...
 4.4.7.17: In Exercises 15 to 18, find the logistic regression function for th...
 4.4.4.18: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.18: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.18: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.18: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.18: In Exercises 17 to 24, sketch the graph of each function. f(x) = 4x
 4.4.3.18: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.18: Compound Interest In Exercises 13 to 20, solve the given problem re...
 4.4.7.18: In Exercises 15 to 18, find the logistic regression function for th...
 4.4.4.19: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.19: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.19: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.19: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.19: In Exercises 17 to 24, sketch the graph of each function. f(x) = 10x
 4.4.3.19: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.19: Compound Interest In Exercises 13 to 20, solve the given problem re...
 4.4.7.19: Lift Tickets Prices The following table shows the price of an alld...
 4.4.4.20: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.20: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.20: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.20: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.20: In Exercises 17 to 24, sketch the graph of each function. f(x) = 6x
 4.4.3.20: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.20: Compound Interest In Exercises 13 to 20, solve the given problem re...
 4.4.7.20: Recycling Rates U.S. recycling rates have been increasing over the ...
 4.4.4.21: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.21: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.21: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.21: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.21: In Exercises 17 to 24, sketch the graph of each function. f(x) = a32b
 4.4.3.21: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.21: Continuous Compounding Interest In Exercises 21 to 24, solve the gi...
 4.4.7.21: Hypothermia The following table shows the time T, in hours, before ...
 4.4.4.22: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.22: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.22: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.22: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.22: In Exercises 17 to 24, sketch the graph of each function. f(x) = a52bx
 4.4.3.22: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.22: Continuous Compounding Interest In Exercises 21 to 24, solve the gi...
 4.4.7.22: Atmospheric Pressure The following table shows the Earths atmospher...
 4.4.4.23: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.23: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.23: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.23: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.23: In Exercises 17 to 24, sketch the graph of each function. f(x) = a13bx
 4.4.3.23: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.23: Continuous Compounding Interest In Exercises 21 to 24, solve the gi...
 4.4.7.23: Hypothermia The following table shows the time T, in hours, before ...
 4.4.4.24: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.24: In Exercises 13 to 24, solve each equation. Do not use a calculator...
 4.4.1.24: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.24: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.24: In Exercises 17 to 24, sketch the graph of each function. f(x) = a23bx
 4.4.3.24: In Exercises 13 to 24, write each equation in its logarithmic form....
 4.4.6.24: Continuous Compounding Interest In Exercises 21 to 24, solve the gi...
 4.4.7.24: 400Meter Race The following table lists the progression of world r...
 4.4.4.25: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.25: In Exercises 25 to 36, sketch the graph of each function. f(x) = (2...
 4.4.1.25: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.25: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.25: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.25: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.25: In Exercises 25 to 30, determine the following constants for the gi...
 4.4.7.25: Telecommuting The graph below shows the growth in the number of tel...
 4.4.4.26: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.26: In Exercises 25 to 36, sketch the graph of each function. f(x) = a14bx
 4.4.1.26: In Exercises 17 to 26, use composition of functions to determine wh...
 4.4.5.26: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.26: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.26: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.26: In Exercises 25 to 30, determine the following constants for the gi...
 4.4.7.26: Population of Hawaii The following table shows the population of th...
 4.4.4.27: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.27: In Exercises 25 to 36, sketch the graph of each function. f(x) = 3 x
 4.4.1.27: In Exercises 27 to 30, find the inverse of the function. If the fun...
 4.4.5.27: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.27: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.27: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.27: In Exercises 25 to 30, determine the following constants for the gi...
 4.4.7.27: Optometry The near point p of a person is the closest distance at w...
 4.4.4.28: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.28: In Exercises 25 to 36, sketch the graph of each function. f(x) = 4 x
 4.4.1.28: In Exercises 27 to 30, find the inverse of the function. If the fun...
 4.4.5.28: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.28: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.28: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.28: In Exercises 25 to 30, determine the following constants for the gi...
 4.4.7.28: Chemistry The amount of oxygen x, in milliliters per liter, that ca...
 4.4.4.29: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.29: In Exercises 25 to 36, sketch the graph of each function. f(x) = 2x...
 4.4.1.29: In Exercises 27 to 30, find the inverse of the function. If the fun...
 4.4.5.29: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.29: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.29: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.29: In Exercises 25 to 30, determine the following constants for the gi...
 4.4.7.29: The HendersonHasselbach Function The scientists Henderson and Hass...
 4.4.4.30: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.30: In Exercises 25 to 36, sketch the graph of each function. f(x) = 2(...
 4.4.1.30: In Exercises 27 to 30, find the inverse of the function. If the fun...
 4.4.5.30: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.30: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.30: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.30: In Exercises 25 to 30, determine the following constants for the gi...
 4.4.7.30: World Population The following table lists the years in which the w...
 4.4.4.31: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.31: In Exercises 25 to 36, sketch the graph of each function. f(x) = lo...
 4.4.1.31: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.31: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.31: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.31: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.31: In Exercises 31 to 34, use algebraic procedures to find the logisti...
 4.4.7.31: Panda Population One estimate gives the world panda population as 3...
 4.4.4.32: In Exercises 17 to 32, write each expression as a single logarithm ...
 4.32: In Exercises 25 to 36, sketch the graph of each function. f(x) = lo...
 4.4.1.32: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.32: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.32: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.32: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.32: In Exercises 31 to 34, use algebraic procedures to find the logisti...
 4.4.7.32: Olympic High Jump The following table on page 415 shows the Olympic...
 4.4.4.33: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.33: In Exercises 25 to 36, sketch the graph of each function. f(x) = 13...
 4.4.1.33: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.33: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.33: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.33: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.33: In Exercises 31 to 34, use algebraic procedures to find the logisti...
 4.4.7.33: Number of Cinema Sites The following table shows the number of U.S....
 4.4.4.34: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.34: In Exercises 25 to 36, sketch the graph of each function. f(x) = 3 ...
 4.4.1.34: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.34: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.34: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.34: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.34: In Exercises 31 to 34, use algebraic procedures to find the logisti...
 4.4.7.34: Temperature of Coffee A cup of coffee is placed in a room that main...
 4.4.4.35: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.35: In Exercises 25 to 36, sketch the graph of each function. f(x) = 12...
 4.4.1.35: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.35: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.35: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.35: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.35: Revenue The annual revenue R, in dollars, of a new company can be c...
 4.4.7.35: World Population The following table lists the years in which the w...
 4.4.4.36: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.36: In Exercises 25 to 36, sketch the graph of each function. f(x) = ln x
 4.4.1.36: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.36: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.36: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.36: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.36: New Car Sales The number of cars A sold annually by an automobile d...
 4.4.7.36: A Correlation Coefficient of 1 A scientist uses a graphing calculat...
 4.4.7.37: Duplicate Data Points An engineer needs to model the data in set A ...
 4.4.4.37: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.37: In Exercises 37 and 38, use a graphing utility to graph each functi...
 4.4.1.37: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.37: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.37: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.37: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.37: Population Growth In exercises 37 to 40, solve the given problem re...
 4.4.7.38: Domain Error A scientist needs to model the data in set A. A = 5(0,...
 4.4.4.38: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.38: In Exercises 37 and 38, use a graphing utility to graph each functi...
 4.4.1.38: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.38: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.38: In Exercises 25 to 38, explain how to use the graph of the first fu...
 4.4.3.38: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.38: Population Growth In exercises 37 to 40, solve the given problem re...
 4.4.7.39: Power Functions A function that can be written in the form is said ...
 4.4.4.39: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.39: In Exercises 39 to 42, change each logarithmic equation to its expo...
 4.4.1.39: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.39: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.39: In Exercises 39 to 46, use a graphing utility to graph each functio...
 4.4.3.39: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.39: Population Growth In exercises 37 to 40, solve the given problem re...
 4.4.7.40: Period of a Pendulum The following table shows the time t (in secon...
 4.4.4.40: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.40: In Exercises 39 to 42, change each logarithmic equation to its expo...
 4.4.1.40: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.40: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.40: In Exercises 39 to 46, use a graphing utility to graph each functio...
 4.4.3.40: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.40: Population Growth In exercises 37 to 40, solve the given problem re...
 4.4.4.41: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.41: In Exercises 39 to 42, change each logarithmic equation to its expo...
 4.4.1.41: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.41: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.41: In Exercises 39 to 46, use a graphing utility to graph each functio...
 4.4.3.41: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.41: Physics Newtons Law of Cooling states that if an object at temperat...
 4.4.4.42: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.42: In Exercises 39 to 42, change each logarithmic equation to its expo...
 4.4.1.42: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.42: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.42: In Exercises 39 to 46, use a graphing utility to graph each functio...
 4.4.3.42: In Exercises 25 to 42, evaluate each logarithm. Do not use a calcul...
 4.4.6.42: Psychology According to a software company, the users of its typing...
 4.4.4.43: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.43: In Exercises 43 to 46, change each exponential equation to its loga...
 4.4.1.43: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.43: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.43: In Exercises 39 to 46, use a graphing utility to graph each functio...
 4.4.3.43: In Exercises 43 to 50, graph each function by using its exponential...
 4.4.6.43: Psychology In the city of Whispering Palms, which has a population ...
 4.4.4.44: In Exercises 33 to 44, use the changeofbase formula to approximat...
 4.44: In Exercises 43 to 46, change each exponential equation to its loga...
 4.4.1.44: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.44: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.44: In Exercises 39 to 46, use a graphing utility to graph each functio...
 4.4.3.44: In Exercises 43 to 50, graph each function by using its exponential...
 4.4.6.44: Law A lawyer has determined that the number of people in a city of ...
 4.4.4.45: In Exercises 45 to 52, use a graphing utility and the changeofbas...
 4.45: In Exercises 43 to 46, change each exponential equation to its loga...
 4.4.1.45: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.45: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.45: In Exercises 39 to 46, use a graphing utility to graph each functio...
 4.4.3.45: In Exercises 43 to 50, graph each function by using its exponential...
 4.4.6.45: Depreciation An automobile depreciates according to the function V(...
 4.4.4.46: In Exercises 45 to 52, use a graphing utility and the changeofbas...
 4.46: In Exercises 43 to 46, change each exponential equation to its loga...
 4.4.1.46: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.46: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.46: In Exercises 39 to 46, use a graphing utility to graph each functio...
 4.4.3.46: In Exercises 43 to 50, graph each function by using its exponential...
 4.4.6.46: Physics The current (measured in amperes) of a circuit is given by ...
 4.4.4.47: In Exercises 45 to 52, use a graphing utility and the changeofbas...
 4.47: In Exercises 47 to 50, expand the given logarithmic expression. log...
 4.4.1.47: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.47: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.47: E. Coli Infection Escherichia coli (E. coli) is a bacterium that ca...
 4.4.3.47: In Exercises 43 to 50, graph each function by using its exponential...
 4.4.6.47: Air Resistance In Exercises 47 to 50, solve the given problems rela...
 4.4.4.48: In Exercises 45 to 52, use a graphing utility and the changeofbas...
 4.48: In Exercises 47 to 50, expand the given logarithmic expression. log...
 4.4.1.48: In Exercises 31 to 48, find f 1(x). State any restrictions on the d...
 4.4.5.48: In Exercises 1 to 48, use algebraic procedures to find the = 70 exa...
 4.4.2.48: Medication in the Bloodstream The exponential function A(t) = 200e...
 4.4.3.48: In Exercises 43 to 50, graph each function by using its exponential...
 4.4.6.48: Air Resistance In Exercises 47 to 50, solve the given problems rela...
 4.4.4.49: In Exercises 45 to 52, use a graphing utility and the changeofbas...
 4.49: In Exercises 47 to 50, expand the given logarithmic expression. ln xy3
 4.4.1.49: Fahrenheit to Celsius The function f(x) = 59 (x  32) is used to co...
 4.4.5.49: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.49: Demand for a Product The demand d for a specific product, in items ...
 4.4.3.49: In Exercises 43 to 50, graph each function by using its exponential...
 4.4.6.49: Air Resistance In Exercises 47 to 50, solve the given problems rela...
 4.4.4.50: In Exercises 45 to 52, use a graphing utility and the changeofbas...
 4.50: In Exercises 47 to 50, expand the given logarithmic expression. ln1...
 4.4.1.50: Retail Sales A clothing merchant uses the function S(x) = 32 x + 18...
 4.4.5.50: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.50: Sales The monthly income I, in dollars, from a new product is given...
 4.4.3.50: In Exercises 43 to 50, graph each function by using its exponential...
 4.4.6.50: Air Resistance In Exercises 47 to 50, solve the given problems rela...
 4.4.4.51: In Exercises 45 to 52, use a graphing utility and the changeofbas...
 4.51: In Exercises 51 to 54, write each logarithmic expression as a singl...
 4.4.1.51: Fashion The function s(x) = 2x + 24 can be used to convert a U.S. w...
 4.4.5.51: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.51: Photochromatic Eyeglass Lenses Photochromatic eyeglass lenses conta...
 4.4.3.51: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.51: Learning Theory The logistic model is also used in learning theory....
 4.4.4.52: In Exercises 45 to 52, use a graphing utility and the changeofbas...
 4.52: In Exercises 51 to 54, write each logarithmic expression as a singl...
 4.4.1.52: Fashion The function K(x) = 1.3x  4.7 converts a mens shoe size in...
 4.4.5.52: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.52: Radiation Lead shielding is used to contain radiation. The percenta...
 4.4.3.52: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.52: Learning Theory A company provides training in the assembly of a co...
 4.4.4.53: In Exercises 53 to 62, determine whether the statement is true or f...
 4.53: In Exercises 51 to 54, write each logarithmic expression as a singl...
 4.4.1.53: Catering A catering service uses the function c(x) = 300 + 12xx to ...
 4.4.5.53: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.53: The Pay It Forward Model In the movie Pay It Forward, Trevor McKinn...
 4.4.3.53: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.53: Medication Level A patient is given three doses of aspirin. Each do...
 4.4.4.54: In Exercises 53 to 62, determine whether the statement is true or f...
 4.54: In Exercises 51 to 54, write each logarithmic expression as a singl...
 4.4.1.54: Landscaping A landscaping company uses the function c(x) = 600 + 14...
 4.4.5.54: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.54: Fish Population The number of bass in a lake is given by P(t) = 360...
 4.4.3.54: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.54: Medication Level Use the dosage formula in Exercise 53 to determine...
 4.4.4.55: In Exercises 53 to 62, determine whether the statement is true or f...
 4.55: In Exercises 55 to 58, use the changeofbase formula and a calcula...
 4.4.1.55: Compensation The monthly earnings in dollars, of a software sales e...
 4.4.5.55: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.55: A Temperature Model A cup of coffee is heated to 180F and placed in...
 4.4.3.55: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.55: Annual Growth Rate The exponential growth function for the populati...
 4.4.4.56: In Exercises 53 to 62, determine whether the statement is true or f...
 4.56: In Exercises 55 to 58, use the changeofbase formula and a calcula...
 4.4.1.56: Grading A professor uses the function defined by the following tabl...
 4.4.5.56: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.56: Intensity of Light The percent of the original intensity of light s...
 4.4.3.56: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.56: Oil Spills Crude oil leaks from a tank at a rate that depends on th...
 4.4.4.57: In Exercises 53 to 62, determine whether the statement is true or f...
 4.57: In Exercises 55 to 58, use the changeofbase formula and a calcula...
 4.4.1.57: The Birthday famous problem called the birthday problem goes like t...
 4.4.5.57: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.57: Musical Scales Starting on the left side of a standard 88key piano...
 4.4.3.57: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.57: If P0>c (which implies that 1<a<0), then the logistic function P(t)...
 4.4.4.58: In Exercises 53 to 62, determine whether the statement is true or f...
 4.58: In Exercises 55 to 58, use the changeofbase formula and a calcula...
 4.4.1.58: Medication Level The function shown in the following graph models t...
 4.4.5.58: In Exercises 49 to 58, use a graphing utility to approximate the so...
 4.4.2.58: In Exercises 58 and 59, verify that the given function is odd or ev...
 4.4.3.58: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.58: If P0>c (which implies that 1<a<0), then the logistic function P(t)...
 4.4.4.59: In Exercises 53 to 62, determine whether the statement is true or f...
 4.59: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.59: Cryptology Cryptology is the study of making and breaking secret co...
 4.4.5.59: Population Growth The population P of a city grows exponentially ac...
 4.4.2.59: In Exercises 58 and 59, verify that the given function is odd or ev...
 4.4.3.59: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.6.59: If P0>c (which implies that 1<a<0), then the logistic function P(t)...
 4.4.4.60: In Exercises 53 to 62, determine whether the statement is true or f...
 4.60: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.60: Cryptography A friend is using the letternumber correspondence in E...
 4.4.5.60: Physical Fitness After a race, a runners pulse rate R, in beats per...
 4.4.2.60: In Exercises 60 and 61, draw the graphs as indicated. Graph g(x) = ...
 4.4.3.60: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.4.61: In Exercises 53 to 62, determine whether the statement is true or f...
 4.61: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.61: In Exercises 61 to 66, answer the question without finding the equa...
 4.4.5.61: Rate of Cooling A can of soda at 79F is placed in a refrigerator th...
 4.4.2.61: In Exercises 60 and 61, draw the graphs as indicated. Graph f(x) = ...
 4.4.3.61: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.4.62: In Exercises 53 to 62, determine whether the statement is true or f...
 4.62: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.62: In Exercises 61 to 66, answer the question without finding the equa...
 4.4.5.62: Medicine During surgery, a patients circulatory system requires at ...
 4.4.2.62: In Exercises 62 to 65, determine the domain of the given function. ...
 4.4.3.62: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.4.63: In Exercises 63 and 64, evaluate the given expression without using...
 4.63: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.63: In Exercises 61 to 66, answer the question without finding the equa...
 4.4.5.63: Bertalanffys Equation In 1938, the biologist Ludwig von Bertalanffy...
 4.4.2.63: In Exercises 62 to 65, determine the domain of the given function. ...
 4.4.3.63: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.4.64: In Exercises 63 and 64, evaluate the given expression without using...
 4.64: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.64: In Exercises 61 to 66, answer the question without finding the equa...
 4.4.5.64: Bertalanffys Equation In 1938, the biologist Ludwig von Bertalanffy...
 4.4.2.64: In Exercises 62 to 65, determine the domain of the given function. ...
 4.4.3.64: In Exercises 51 to 64, find the domain of the function. Write the d...
 4.4.4.65: Which is larger, 500501 or 506500? These numbers are too large for ...
 4.65: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.65: Only onetoone functions have inverses that are functions. In Exer...
 4.4.5.65: Typing Speed The following function models the average typing speed...
 4.4.2.65: In Exercises 62 to 65, determine the domain of the given function. ...
 4.4.3.65: In Exercises 65 to 72, use translations of the graphs in Exercises ...
 4.4.4.66: Which is smaller, or See the hint in Exercise 65. 1 151233 ? 1 50300
 4.66: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.66: Only onetoone functions have inverses that are functions. In Exer...
 4.4.5.66: Walking Speed An approximate relation between the average pedestria...
 4.4.2.66: Average Height Explain why the graph of f(x) = ex + ex2 can be pro...
 4.4.3.66: In Exercises 65 to 72, use translations of the graphs in Exercises ...
 4.4.4.67: Earthquake Magnitude The Baja California earthquake of November 20,...
 4.67: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.67: Only onetoone functions have inverses that are functions. In Exer...
 4.4.5.67: Drag Racing The quadratic function s1(x) = 2.25x2 + 56.26x  0.28,...
 4.4.3.67: In Exercises 65 to 72, use translations of the graphs in Exercises ...
 4.4.4.68: Earthquake Magnitude The Colombia earthquake of 1906 had an intensi...
 4.68: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.68: Only onetoone functions have inverses that are functions. In Exer...
 4.4.5.68: Eiffel Tower The functions h1(x) = 363.4  88.4 ln x, 16.47 6 x 61....
 4.4.3.68: In Exercises 65 to 72, use translations of the graphs in Exercises ...
 4.4.4.69: Earthquake Intensity The Coalinga, California, earthquake of 1983 h...
 4.69: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.69: Consider the linear function f(x) = mx + b, m Z 0. The graph of has...
 4.4.5.69: Psychology Industrial psychologists study employee training program...
 4.4.3.69: In Exercises 65 to 72, use translations of the graphs in Exercises ...
 4.4.4.70: Earthquake Intensity The earthquake that occurred just south of Con...
 4.70: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.70: Find the inverse of f(x) = ax2 + bx + c, a Z 0, x  b2a.
 4.4.5.70: Psychology An industrial psychologist has determined that the avera...
 4.4.3.70: In Exercises 65 to 72, use translations of the graphs in Exercises ...
 4.4.4.71: Comparison of Earthquakes Compare the intensity of an earthquake th...
 4.71: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.71: Use a graph of f(x) = x + 3 to explain why f is its own inverse.
 4.4.5.71: Ecology A herd of bison was placed in a wildlife preserve that can ...
 4.4.3.71: In Exercises 65 to 72, use translations of the graphs in Exercises ...
 4.4.4.72: Comparison of Earthquakes How many times as great was the intensity...
 4.72: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.1.72: Use a graph of f(x) = 216  x2, with 0 x 4, to explain why f is its...
 4.4.5.72: Population Growth A yeast culture grows according to the equation Y...
 4.4.3.72: In Exercises 65 to 72, use translations of the graphs in Exercises ...
 4.4.4.73: Comparison of Earthquakes On March 2, 1933, an earthquake of magnit...
 4.73: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.5.73: Consumption of Natural Resources A model for how long our coal reso...
 4.4.3.73: In Exercises 73 and 74, examine the four functions and the graphs l...
 4.4.4.74: Comparison of Earthquakes An earthquake that occurred in China in 1...
 4.74: In Exercises 59 to 74, solve each equation for x. Give exact answer...
 4.4.5.74: Effects of Air Resistance on Velocity If we assume that air resista...
 4.4.3.74: In Exercises 73 and 74, examine the four functions and the graphs l...
 4.4.4.75: Earthquake Magnitude Find the Richter scale magnitude of the earthq...
 4.75: Earthquake Magnitude Determine, to the nearest 0.1, the Richter sca...
 4.4.5.75: Terminal Velocity with Air Resistance The velocity v, in feet per s...
 4.4.3.75: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.76: Earthquake Magnitude Find the Richter scale magnitude of the earthq...
 4.76: Earthquake Magnitude A seismogram has an amplitude of 18 millimeter...
 4.4.5.76: Effects of Air Resistance on Distance The distance s, in feet, that...
 4.4.3.76: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.77: pH Milk of magnesia has a hydroniumion concentration of about 3.97...
 4.77: Comparison of Earthquakes An earthquake had a Richter scale magnitu...
 4.4.5.77: Retirement Planning The retirement account for a graphic designer c...
 4.4.3.77: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.78: pH Vinegar has a hydroniumion concentration of 1.26 * 103mole per...
 4.78: Comparison of Earthquakes An earthquake has an intensity 600 times ...
 4.4.5.78: Hanging Cable The height h, in feet, of any point P on the cable sh...
 4.4.3.78: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.79: HydroniumIon Concentration A morphine solution has a pH of 9.5. De...
 4.79: Chemistry Find the pH of tomatoes that have a hydroniumion concentr...
 4.4.5.79: The following argument seems to indicate that 0.125 7 0.25. Find th...
 4.4.3.79: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.80: HydroniumIon Concentration A rainstorm in New York City produced r...
 4.80: Chemistry Find the hydroniumion concentration of rainwater that ha...
 4.4.5.80: The following argument seems to indicate that . Find the first inco...
 4.4.3.80: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.81: Decibel Level The range of sound intensities that the human ear can...
 4.81: Compound Interest Find the balance when $16,000 is invested at an a...
 4.4.5.81: A common mistake that students make is to write log(x + y) as log x...
 4.4.3.81: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.82: Decibel Level The range of sound intensities that the human ear can...
 4.82: Compound Interest Find the balance when $19,000 is invested at an a...
 4.4.5.82: Let f(x) = 2 ln x and g(x) = ln x2. Does f(x) = g(x) for all x?
 4.4.3.82: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.83: Decibel Level The range of sound intensities that the human ear can...
 4.83: Depreciation The scrap value S of a product with an expected life s...
 4.4.5.83: Explain why the functions F(x) = 1.4x and G(x) = e0.336x represent ...
 4.4.3.83: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.84: Decibel Level The range of sound intensities that the human ear can...
 4.84: A skin wound heals according to the function given by N(t) = N0e0....
 4.4.5.84: Find k such that f(t) = 2.2t and g(t) = ekt represent essentially ...
 4.4.3.84: In Exercises 75 to 84, use a graphing utility to graph the function...
 4.4.4.85: Animated Maps A software company that creates interactive maps for ...
 4.85: In Exercises 85 to 88, find the exponential growth or decay functio...
 4.4.3.85: Money Market Rates The function r(t) = 0.69607 + 0.60781 ln t gives...
 4.4.4.86: Animated Maps Use the equation in Exercise 85 to determine the scal...
 4.86: In Exercises 85 to 88, find the exponential growth or decay functio...
 4.4.3.86: Average Typing Speed The following function models the average typi...
 4.4.4.87: Prove the quotient property of logarithms logbMN = logb M  logb N ...
 4.87: In Exercises 85 to 88, find the exponential growth or decay functio...
 4.4.3.87: Advertising Costs and Sales The function N(x) = 2750 + 180 lna x100...
 4.4.4.88: Prove the power property of logarithms logb (M p) = p logb M See th...
 4.88: In Exercises 85 to 88, find the exponential growth or decay functio...
 4.4.3.88: Medicine In anesthesiology it is necessary to accurately estimate t...
 4.89: Population Growth a. Find the exponential growth function for a cit...
 4.4.3.89: Medicine In anesthesiology it is necessary to accurately estimate t...
 4.90: Carbon Dating Determine, to the nearest 10 years, the age of a bone...
 4.4.3.90: Astronomy Astronomers measure the apparent brightness of a star by ...
 4.91: Cellular Telephone Subscribership The following table shows the num...
 4.4.3.91: Number of Digits in b X An engineer has determined that the number ...
 4.92: Mortality Rate The following table shows the infant mortality rate ...
 4.4.3.92: Number of Digits in 9(99) A science teacher has offered 10 points e...
 4.93: Logistic Growth The population of coyotes in a national park satisf...
 4.4.3.93: In Exercises 93 and 94, use a graphing utility to determine the rel...
 4.94: Logistic Growth Consider the logistic function P(t) = 1281 + 5e0.2...
 4.4.3.94: In Exercises 93 and 94, use a graphing utility to determine the rel...
 4.4.3.95: The functions f(x) = ex  e xe x + ex and g(x) = 12ln1 + x1  x a...
 4.4.3.96: Use a graph of f(x) = 2ex + exto determine the domain and range of f.
Solutions for Chapter 4: Exponential and Logarithmic Functions
Full solutions for College Algebra  7th Edition
ISBN: 9781439048610
Solutions for Chapter 4: Exponential and Logarithmic Functions
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Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Outer product uv T
= column times row = rank one matrix.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.