SECTION 5.9 Building Exponential, Logarithmic, and Logistic Models from Data 373 11. Mixed Practice Golfing The data below represent the expected percentage of putts that will be made by professional golfers on the PGA Tour, depending on distance. For example, it is expected that 99.3% of 2-foot putts will be made. Distance (feet) Expected Percentage Distance (feet) Expected Percentage 2 99.3 14 25.0 3 94.8 15 22.0 4 85.8 16 20.0 5 74.7 17 19.0 6 64.7 18 17.0 7 55.6 19 16.0 8 48.5 20 14.0 9 43.4 21 13.0 10 38.3 22 12.0 11 34.2 23 11.0 12 30.1 24 11.0 13 27.0 25 10.0 Source: TheSandTrap.com (a) Using a graphing utility, draw a scatter plot of the data with distance as the independent variable. (b) Based on the scatter plot drawn in part (a), decide on a model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between distance and expected percentage. Be sure to justify your choice of model. (c) Using a graphing utility, find the model of best fit. (d) Graph the function found in part (c) on the scatter plot. (e) Use the function found in part (c) to predict what percentage of 30-foot putts will be made. (a) Using a graphing utility, draw a scatter plot of the data treating temperature as the independent variable and chirps per second as the dependent variable. (b) Based on the scatter plot drawn in part (a), decide what model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between temperature and chirps per second. (c) Using a graphing utility, find the model of best fit. (d) Using a graphing utility, graph the function found in part (c) on the scatter plot drawn in part (a). (e) Use your model to predict the chirps per second if the temperature is 80 degrees Fahrenheit. 10. Mixed Practice Age versus Total Cholesterol The data below represent the age and average total cholesterol for adult males at various ages. Age Total Cholesterol 27 40 50 60 70 80 189 205 215 210 210 194 (a) Using a graphing utility, draw a scatter plot of the data using age, x, as the independent variable and total cholesterol, y, as the dependent variable. (b) Based on the scatter plot drawn in part (a), decide on a model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between age and total cholesterol. Be sure to justify your choice of model. (c) Using a graphing utility, find the model of best fit. (d) Using a graphing utility, graph the function found in part (c) on the scatter plot drawn in part (a). (e) Use your model to predict the total cholesterol of a 35-year-old male. Retain Your Knowledge Problems 12–21 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. 12. Construct a polynomial function that might have the graph shown. (More than one answer is possible.) x y 2 4 –4 –2 4 2 –4 –2 13. Use the Pythagorean Theorem to find the exact length of the unlabeled side in the given right triangle. 1 2 14. Graph the equation ( ) − + = x y 3 25. 2 2 15. Find the midpoint of the line segment with endpoints ( ) −7, 5 and ( ) − 1, 9. (continued)
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