Applied Calculus 5th Edition solutions

Applied Calculus 5
Table A.5 gives the gross world product, G, which measures global output of goods and services.3 If t is in years since 1950, the regression line for these data is G = 3.543 + 0.734t. (a) Plot the data and the regression line on the same axes. Does the line fit the data well? (b) Interpret the slope

Applied Calculus 5
Table A.6 shows worldwide cigarette production as a function of t, the number of years since 1950.4 (a) Find the regression line for this data. (b) Use the regression line to estimate world cigarette production in the year 2010. (c) Interpret the slope of the line in terms of cigarette production. (d

Applied Calculus 5
Table A.7 shows the US Gross National Product (GNP).5 (a) Plot GNP against years since 1970. Does a line fit the data well? (b) Find the regression line and graph it with the data. (c) Use the regression line to estimate the GNP in 1985 and in 2020. Which estimate do you have more confidence in? Why?

Applied Calculus 5
The acidity of a solution is measured by its pH, with lower pH values indicating more acidity. A study of acid rain was undertaken in Colorado between 1975 and 1978, in which the acidity of rain was measured for 150 consecutive weeks.6 The data followed a generally linear pattern. If P is the pH and

Applied Calculus 5
In a 1977 study7 of 21 of the best American female runners, researchers measured the average stride rate, S, at different speeds, v. The data are given in Table A.8. (a) Find the regression line for these data, using stride rate as the dependent variable. (b) Plot the regression line and the data on

Applied Calculus 5
Table A.9 shows the atmospheric concentration of carbon dioxide, CO2 (in parts per million, ppm), at the Mauna Loa Observatory in Hawaii.8 (a) Find the average rate of change of the concentration of carbon dioxide between 1980 and 2000. Give units and interpret your answer in terms of carbon dioxide.

Applied Calculus 5
In Problem 6, carbon dioxide concentration was modeled as a linear function of time. However, if we include data for carbon dioxide concentration from as far back as 1900, the data appear to be more exponential than linear. (They looked linear in Problem 6 because we were only looking at a small piec

Applied Calculus 5
(a) Fit an exponential function to the population data in Table A.10. Plot the data and the exponential function on the same axes. (b) At approximately what percentage rate was the population growing between 1960 and 2000? (c) If the population continues to grow at the same percentage rate, what popu

Applied Calculus 5
Table A.11 shows the public debt, D, of the US9 in billions of dollars, t years after 1998. (a) Plot the public debt against the number of years since 1998. (b) Does the data look more linear or more exponential? (c) Fit an exponential function to the data and graph it with the data. (d) What annual

Applied Calculus 5
A company collects the data in Table A.12. Find the regression line and interpret its slope. Sketch the data and the line. What is the correlation coefficient? Why is the value you get reasonable? Table A.12 Cost to produce various quantities of a product q (quantity in units) 25 50 75 100 125 C (cos

Applied Calculus 5
Match the r values with scatter plots in Figure A.11. r = 0.98, r= 0.5, r= 0.25, r = 0, r= 0.7, r= 1. 2 4 6 8 10 2 4 6 8 10 x (a) y 2 4 6 8 10 2 4 6 8 10 x (b) y 2 4 6 8 10 2 4 6 8 10 x (c) y 2 4 6 8 10 2 4 6 8 10 x (d) y 2 4 6 8 10 2 4 6 8 10 x (e) y 2 4 6 8 10 2 4 6 8 10 x (f) y Figure A.11

Applied Calculus 5
Table A.13 shows the number of cars, N, in millions in the US10 t years after 1940. (a) Plot the data, with number of passenger cars as the dependent variable. (b) Does a linear or exponential model appear to fit the data better? (c) Use a linear model first: Find the regression line for these data.

Applied Calculus 5
Table A.14 gives the population of the world in billions. (a) Plot these data. Does a linear or exponential model seem to fit the data best? (b) Find an exponential regression function. (c) What annual percent growth rate does the exponential function show? (d) Predict the population of the world in

Applied Calculus 5
In 1969, all field goal attempts in the National Football League and American Football League were analyzed. See Table A.15. (The data has been summarized: all attempts between 10 and 19 yards from the goal post are listed as 14.5 yards out, etc. ) (a) Graph the data, with success rate as the depende

Applied Calculus 5
Table A.16 shows the number of Japanese cars imported into the US.11 (a) Plot the number of Japanese cars imported against the number of years since 1964. (b) Does the data look more linear or more exponential? (c) Fit an exponential function to the data and graph it with the data. (d) What annual pe

Applied Calculus 5
Figure A.12 shows oil production in the Middle East.12 If you were to model this function with a polynomial, what degree would you choose? Would the leading coefficient be positive or negative? 1970 1980 1990 0 500 1000 1500 million tons of oil year Figure A.12

Applied Calculus 5
After the oil crisis in 1973, the average fuel efficiency, E, of cars increased until the early 1990s, when it started to decrease again. (a) Plot the data 13 in Table A.17, using t in years since 1975. If you were to fit a quadratic polynomial to the data, what would be the sign of the leading coeff

Applied Calculus 5
Table A.18 gives the area of rain forest destroyed for agriculture and development.14 (a) Plot these data. (b) Are the data increasing or decreasing? Concave up or concave down? In each case, interpret your answer in terms of rain forest. (c) Use a calculator or computer to fit a logarithmic function

Applied Calculus 5
World solar power, S, inmegawatts; t in years since 1990 t 0 1 2 3 4 5 6 7 S 47 55 58 60 69 78 89 126 t 8 9 10 11 12 13 14 15 S 153 201 277 386 547 748 1194 1782

Applied Calculus 5
Nuclear warheads, N, in thousands; t in years since 1960 t 0 5 10 15 20 25 30 35 40 45 N 22 38 39 48 55 65 59 40 33 28

Applied Calculus 5
Carbon dioxide, C, in ppm; t in years since 1970 t 0 5 10 15 20 25 30 35 C 326 331 339 346 354 361 369 380

Applied Calculus 5
For each graph in Figure A.13, decide whether the best fit for the data appears to be a linear function, an exponential function, or a polynomial.