156 CHAPTER 3 Linear and Quadratic Functions Speed Off Bat (mph), s Homerun Distance (feet), d 98 369 99 381 100 380 100 397 101 400 102 383 102 408 104 392 104 406 104 421 105 411 107 396 107 429 109 404 109 418 Source: Statcast 24. Mixed Practice Credit Scores A Fair Isaacs Corporation (FICO) score is used to determine a person’s creditworthiness. An economist wishes to find a function that relates the interest rate (in percent) of a 36-month auto loan, I, to a person’s FICO score, s. Consider the following data. Credit Score, s Interest Rate (percent), I 545 18.982 595 17.967 640 12.218 675 8.612 705 6.680 750 5.150 Source: myfico.com (a) Does the relation defined by the set of ordered pairs ( ) s I , represent a function? (b) Draw a scatter plot of the data. (c) Using a graphing utility, find the line of best fit that models the relation between FICO score and interest rate. (d) Interpret the slope. (e) Express the relationship found in part (c) using function notation. (f) If a person has a FICO score of 718, predict the interest rate. 22. Study Time An educational research project surveyed 12 students in a college course. One of the survey questions asked students how many hours they studied for a chapter test. The table shows the number of hours, x, that each student studied and their corresponding test score, y. Hours Studied, x Test Score, y 1 50 2 55 3 65 3 71 4 68 5 82 6 78 6 88 7 87 8 95 10 93 10 96 (a) Use a graphing utility to draw a scatter plot. (b) Use a graphing utility to find the line of best fit that models the relation between number of hours studied and test score. Express the model using function notation. (c) Interpret the slope of the line of best fit. (d) Use your model from part (b) to predict the test score of a student who studies for 9 hours. (e) Use your model from part (b) to predict how many hours of study time corresponds to a test score of 85. 23. Mixed Practice Homeruns A baseball analyst wishes to find a function that relates the distance, d, of a homerun and the speed, s, of the ball off the bat. Consider the data shown in the next column. (a) Does the relation defined by the set of orders pairs ( ) s d , represent a function? (b) Draw a scatter plot of the data, treating speed off bat as the independent variable. (c) Using a graphing utility, find the line of best fit that models the relation between the speed off the bat and the distance of the homerun? (d) Interpret the slope. (e) Express the relationship found in part (c), using function notation. (f) What is the domain of the function? (g) Predict the homerun distance if the speed of the ball off the bat is 103 miles per hour. Explaining Concepts 25. Find the line of best fit for the ordered pairs ( ) 1, 5 and ( ) 3, 8 . What is the correlation coefficient for these data? Why is this result reasonable? 26. What does a correlation coefficient of 0 imply? 27. Explain why it does not make sense to interpret the y-intercept in Problem 17. 28. Refer to Problem 19. Solve ( ) = G h 0 and provide an interpretation of this result. Find ( ) G 0 and provide an interpretation of this result.
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