Recycling Plastic Bags. It is estimated that 90 billion plastic carry-out bags are

Find each of the following, to four decimal places, using a calculator.e4

Find each of the following, to four decimal places, using a calculator.e10

Find each of the following, to four decimal places, using a calculator.e-2.458

Find each of the following, to four decimal places, using a calculator. a 1 e3 b 2

n Exercises 510, match the function with one of the graphs (a)(f), which follow.f 1x2 = -2x - 1

n Exercises 510, match the function with one of the graphs (a)(f), which follow.f 1x2 = - 11 2 2x

n Exercises 510, match the function with one of the graphs (a)(f), which follow.f 1x2 = ex + 3

n Exercises 510, match the function with one of the graphs (a)(f), which follow.f 1x2 = ex+1

n Exercises 510, match the function with one of the graphs (a)(f), which follow.f 1x2 = 3-x - 2

n Exercises 510, match the function with one of the graphs (a)(f), which follow.f 1x2 = 1 - ex

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = 3x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = 5x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = 6x

Graph the function by substituting and plotting points. Then check your work using a graphing calculator 1x2 = 3-x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = 11 4 2x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = 12 3 2x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatory = -2x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatory = 3 - 3x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = -0.25x + 4

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = 0.6x - 3

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = 1 + e-x

Graph the function by substituting and plotting points. Then check your work using a graphing calculator f 1x2 = 2 - e-x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatory = 1 4 ex

Graph the function by substituting and plotting points. Then check your work using a graphing calculatory = 2e-x

Graph the function by substituting and plotting points. Then check your work using a graphing calculator 1x2 = 1 - e-x

Graph the function by substituting and plotting points. Then check your work using a graphing calculatorf 1x2 = ex - 2

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 2x+1

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 2x-1

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 2x - 3

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 2x + 1

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 21-x + 2

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 5 - 2-x

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 4 - 3-x

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 2x-1 - 3

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 13 2 2x-1

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 34-x

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 2x+3 - 5

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = -3x-2

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 3  2x-1 + 1

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 2  3x+1 - 2

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = e2x

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = e-0.2x

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 1 211 - ex 2

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 311 + ex 2 - 2

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.V

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.y = e2x + 1

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 211 - e-x 2

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function.f 1x2 = 1 - e-0.01x

Graph the piecewise function.1x2 = c e-x - 4, for x 6 -2, x + 3, for -2 x 6 1, x2 , for x 1

Graph the piecewise function.g1x2 = c 4, for x -3, x2 - 6, for -3 6 x 6 0, ex , for x 0

Compound Interest. Suppose that $82,000 is invested at 41 2, interest, compounded quarterly. a) Find the function for the amount to which the investment grows after t years. b) Graph the function. c) Find the amount of money in the account at t = 0, 2, 5, and 10 years. d) When will the amount of money in the account reach $100,000?

Compound Interest. Suppose that $750 is invested at 7% interest, compounded semiannually. a) Find the function for the amount to which the investment grows after t years. b) Graph the function. c) Find the amount of money in the account at t = 1, 6, 10, 15, and 25 years. d) When will the amount of money in the account reach $3000?

Interest on a CD. On Wills sixth birthday, his grandparents present him with a $3000 certificate of deposit (CD) that earns 5% interest, compounded quarterly. If the CD matures on his sixteenth birthday, what amount will be available then?

Interest in a College Trust Fund. Following the birth of her child, Sophia deposits $10,000 in a college trust fund where interest is 3.9%, compounded semiannually. a) Find a function for the amount in the account after t years. b) Find the amount of money in the account at t = 0, 4, 8, 10, and 18 years.

In Exercises 5562, use the compound-interest formula to find the account balance A with the given conditions: P = principal, r = interest rate, n = number of compounding periods per year, t = time, in years, A = account balance. P r Compounded ntA $3,000 4% Semiannually 2 $12,500 3% Quarterly 3 $120,000 2.5% Annually 10 $120,000 2.5% Quarterly 10 $53,500 51 2, Quarterly 61 2 $6,250 63 4, Semiannually 41 2 $17,400 8.1% Daily 5 $900 7.3% Daily 71

In Exercises 5562, use the compound-interest formula to find the account balance A with the given conditions: P = principal, r = interest rate, n = number of compounding periods per year, t = time, in years, A = account balance. P r Compounded ntA $3,000 4% Semiannually 2 $12,500 3% Quarterly 3 $120,000 2.5% Annually 10 $120,000 2.5% Quarterly 10 $53,500 51 2, Quarterly 61 2 $6,250 63 4, Semiannually 41 2 $17,400 8.1% Daily 5 $900 7.3% Daily 71

In Exercises 5562, use the compound-interest formula to find the account balance A with the given conditions: P = principal, r = interest rate, n = number of compounding periods per year, t = time, in years, A = account balance. P r Compounded ntA $3,000 4% Semiannually 2 $12,500 3% Quarterly 3 $120,000 2.5% Annually 10 $120,000 2.5% Quarterly 10 $53,500 51 2, Quarterly 61 2 $6,250 63 4, Semiannually 41 2 $17,400 8.1% Daily 5 $900 7.3% Daily 71

In Exercises 5562, use the compound-interest formula to find the account balance A with the given conditions: P = principal, r = interest rate, n = number of compounding periods per year, t = time, in years, A = account balance. P r Compounded ntA $3,000 4% Semiannually 2 $12,500 3% Quarterly 3 $120,000 2.5% Annually 10 $120,000 2.5% Quarterly 10 $53,500 51 2, Quarterly 61 2 $6,250 63 4, Semiannually 41 2 $17,400 8.1% Daily 5 $900 7.3% Daily 71

In Exercises 5562, use the compound-interest formula to find the account balance A with the given conditions: P = principal, r = interest rate, n = number of compounding periods per year, t = time, in years, A = account balance. P r Compounded ntA $3,000 4% Semiannually 2 $12,500 3% Quarterly 3 $120,000 2.5% Annually 10 $120,000 2.5% Quarterly 10 $53,500 51 2, Quarterly 61 2 $6,250 63 4, Semiannually 41 2 $17,400 8.1% Daily 5 $900 7.3% Daily 71

In Exercises 5562, use the compound-interest formula to find the account balance A with the given conditions: P = principal, r = interest rate, n = number of compounding periods per year, t = time, in years, A = account balance. P r Compounded ntA $3,000 4% Semiannually 2 $12,500 3% Quarterly 3 $120,000 2.5% Annually 10 $120,000 2.5% Quarterly 10 $53,500 51 2, Quarterly 61 2 $6,250 63 4, Semiannually 41 2 $17,400 8.1% Daily 5 $900 7.3% Daily 71

In Exercises 5562, use the compound-interest formula to find the account balance A with the given conditions: P = principal, r = interest rate, n = number of compounding periods per year, t = time, in years, A = account balance. P r Compounded ntA $3,000 4% Semiannually 2 $12,500 3% Quarterly 3 $120,000 2.5% Annually 10 $120,000 2.5% Quarterly 10 $53,500 51 2, Quarterly 61 2 $6,250 63 4, Semiannually 41 2 $17,400 8.1% Daily 5 $900 7.3% Daily 71

In Exercises 5562, use the compound-interest formula to find the account balance A with the given conditions: P = principal, r = interest rate, n = number of compounding periods per year, t = time, in years, A = account balance. P r Compounded ntA $3,000 4% Semiannually 2 $12,500 3% Quarterly 3 $120,000 2.5% Annually 10 $120,000 2.5% Quarterly 10 $53,500 51 2, Quarterly 61 2 $6,250 63 4, Semiannually 41 2 $17,400 8.1% Daily 5 $900 7.3% Daily 71

Overweight Troops. The number of U.S. troops diagnosed as overweight has more than doubled since 1998 (Source: U.S. Department of Defense). The exponential function W1x2 = 23,672.1611.1122x , where x is the number of years since 1998, can be used to estimate the number of overweight active troops. Find the number of overweight troops in 2000, in 2008, and in 2013.

Foreign Students from India. The number of students from India enrolled in U.S. colleges and universities has grown exponentially from about 9000 in 1980 to about 95,000 in 2008 (Source: Institute of International Education, New York). The exponential function I1t2 = 900011.08782t , where t is the number of years since 1980, can be used to estimate the number of students from India enrolled in U.S. colleges and universities. Find the number of students from India enrolled in 1985, in 1999, in 2006, and in 2012.

RS Tax Code. The number of pages in the IRS Tax Code has increased from 400 pages in 1913 to 70,320 pages in 2009 (Source: IRS). The increase can be modeled by the exponential function T1x2 = 40011.0552x , where x is the number of years since 1913. Use this function to estimate the number of pages in the tax code for 1950, for 1990, and for 2000. Round to the nearest one.

Medicare Premiums. The monthly Medicare Part B health-care premium for most benefi- ciaries ages 65 and older has increased signifi- cantly since 1975. The monthly premium has increased from about $7 in 1975 to $110.50 in 2011 (Source: Centers for Medicare and Medicaid Services). The following exponential function models the premium increases: M1x2 = 711.0802x , where x is the number of years since 1975. Estimate the monthly Medicare Part B premium in 1985, in 1992, and in 2002. Round to the nearest dollar.

Taxi Medallions. The business of taxi medallions, required licenses fastened to the hood of all New York City cabs, has proven itself to be a valuable investment. The average price for a corporate-license taxi medallion in New York has risen from about $200,000 in 2001 to $753,000 in 2009 (Sources: New York City Taxi & Limousine Commission; Andrew Murstein, president of Medallion Financial). The exponential function M1x2 = 200,00011.18022x , where x is the number of years since 2001, models the data for the average price of a medallion in recent years. Estimate the price of a taxi medallion in 2003, in 2007, and in 2013. Round to the nearest dollar.

Cost of Census. The cost per household for taking the U.S. census has increased exponentially since 1970 (Source: GAO analysis of U.S. Census Bureau data). The following function models the increase in cost: C1x2 = 15.520211.05082x , where x is the number of years since 1970. Estimate the cost per household in 1990 and in 2010.

Recycling Plastic Bags. It is estimated that 90 billion plastic carry-out bags are produced annually in the United States. In recent years, the number of tons of plastic bags that are recycled has grown exponentially from approximately 80,000 tons in 1996 to 380,000 tons in 2007. (Source: Environmental Protection Agency) The following exponential function models the amount recycled, in tons: R1x2 = 80,00011.15222x , where x is the number of years since 1996. Find the total amount recycled, in tons, in 1999, in 2007, and in 2012. Then use the function to estimate the total number of tons that will be recycled in 2012.

Masters Degrees Earned by Women. The function D1t2 = 43.122411.04752t gives the number of masters degrees, in thousands, conferred on women in the United States t years after 1960 (Sources: National Center for Educational Statistics; Digest of Education Statistics). Find the number of masters degrees earned by women in 1984, in 2002, and in 2010. Then estimate the number of masters degrees that will be earned by women in 2015.

Tennis Participation. In recent years, U.S. tennis participation has increased. The function T1x2 = 23.762411.07522x , where T1x2 is in millions and x is the number of years since 2006, models the number of people who had played tennis at least once in the year (Source: USTA/Coyne Public Relations). Estimate the number who had played tennis at least once in a year for 2007. Then use this function to project participation in tennis in 2014.

Charitable Giving. Over the last four decades, charitable giving in the United States has grown exponentially from approximately $20.7 billion in 1969 to approximately $303.8 billion in 2009 (Sources: Giving USA Foundation; Volunteering in America by the Corporation for National & Community Service). The function G1x2 = 20.711.069462x , where x is the number of years since 1969, can be used to estimate charitable giving, in billions of dollars. Find the amount of charitable giving in 1978, in 1985, and in 2000.

Salvage Value. A landscape company purchased a backhoe for $56,395. The value of the backhoe each year is 90% of the value of the preceding year. After t years, its value, in dollars, is given by the exponential function V1t2 = 56,39510.92t . a) Graph the function. b) Find the value of the backhoe after 0, 1, 3, 6, and 10 years. Round to the nearest dollar. c) The company decides to replace the backhoe when its value has declined to $30,000. After how long will the machine be replaced?

Salvage Value. A restaurant purchased a 72-in. range with six burners for $6982. The value of the range each year is 85% of the value of the preceding year. After t years, its value, in dollars, is given by the exponential function V1t2 = 698210.852t . a) Graph the function. b) Find the value of the range after 0, 1, 2, 5, and 8 years. c) The restaurant decides to replace the range when its value has declined to $1000. After how long will the range be replaced?

Advertising. A company begins an Internet advertising campaign to market a new phone. The percentage of the target market that buys a product is generally a function of the length of the advertising campaign. The estimated percentage is given by f 1t2 = 10011 - e-0.04t 2, where t is the number of days of the campaign. a) Graph the function. b) Find f 1252, the percentage of the target market that has bought the phone after a 25-day advertising campaign. c) After how long will 90% of the target market have bought the phone?

Growth of a Stock. The value of a stock is given by the function V1t2 = 5811 - e-1.1t 2 + 20, where V is the value of the stock after time t, in months. a) Graph the function. b) Find V112, V122, V142, V162, and V1122. c) After how long will the value of the stock be $75?

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.y = 3x - 3-x

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.y = 3-1x+122

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.f 1x2 = -2.3x

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.f 1x2 = 30,00011.42x

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.y = 2-x 8

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.y = 2-1x-12

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.f 1x2 = 10.582x - 1

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.. y = 2x + 2-x

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.g1x2 = ex

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.f 1x2 = 2x - 1

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.y = 2-x2

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.y = 2x2 - 8

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.g1x2 = ex - e-x 2

In Exercises 7790, use a graphing calculator to match the equation with one of the figures (a)(n), which follow.f 1x2 = ex + e-x 2

Use a graphing calculator to find the point(s) of intersection of the graphs of each of the following pairs of equations.y = 1 - 3x , y = 4 + 3-x2

Use a graphing calculator to find the point(s) of intersection of the graphs of each of the following pairs of equations.y = 4x + 4-x , y = 8 - 2x - x2

Use a graphing calculator to find the point(s) of intersection of the graphs of each of the following pairs of equations.y = 2ex - 3, y = ex x

Use a graphing calculator to find the point(s) of intersection of the graphs of each of the following pairs of equations.y = 1 ex + 1 , y = 0.3x + 7 9

Solve graphically.5.3x - 4.2x = 1073

Solve graphically.ex = x3

Solve graphically.2x 7 1

Solve graphically.3x 1

Solve graphically.2x + 3x = x2 + x3

Solve graphically.31,245e-3x = 523,467

Simplify.11 - 4i217 + 6i2

Simplify.2 - i 3 + i

Find the x-intercepts and the zeros of the function.f 1x2 = 2x2 - 13x - 7

Find the x-intercepts and the zeros of the function.h1x2 = x3 - 3x2 + 3x - 1

Find the x-intercepts and the zeros of the function.h1x2 = x4 - x2

Find the x-intercepts and the zeros of the function.g1x2 = x3 + x2 - 12x

Solve. x3 + 6x2 - 16x = 0

Solve.3x2 - 6 = 5x

Which is larger, 7p or p7 ? 7080 or 8070?

In Exercises 110 and 111: a) Graph using a graphing calculator. b) Approximate the zeros. c) Approximate the relative maximum and minimum values. If your graphing calculator has a MAXMIN feature, use it.f 1x2 = x2 e-x

In Exercises 110 and 111: a) Graph using a graphing calculator. b) Approximate the zeros. c) Approximate the relative maximum and minimum values. If your graphing calculator has a MAXMIN feature, use it.f 1x2 = e-x 2

Graph f 1x2 = x1>1x-12 for x 7 0. Use a graphing calculator and the TABLE feature to identify the horizontal asymptote.

For the function f, construct and simplify the difference quotient. (See Section 2.2 for review.) f 1x2 = 2ex - 3