Explanation Given information: It is provided that the U.S prison population was 475 , 000 and increasing at a rate of 35 , 000 per year. Formula used: The steps for solving the related rate problem are: Step1: List the changing and related quantities followed by restating the problem in rate of change of terms. Step 2: Rewrite the problem using for the changing quantities for their derivatives. Step 3: If possible draw the diagram of the changing quantities and find an equation relating the changing quantities. Step 4: Differentiate with respect to the equation (s) in order to get rate of change in relating quantity. Step 5: Now substitute the values of the provided quantity and their derivative into the derived equation and solve them to get answer. The model for U.S prison population and the average combined SAT score in the United States in 1970 s and 1980 s is given by: S ( n ) = 904 + 1 , 326 ( n − 180 ) 1.325 ( 192 ≤ n ≤ 563 ) Where S ( n ) is the combined average SAT score at a time when the total prison population is n thousand. Calculation: Consider the steps of the formula: The changing quantities are S and n . Since, the U.S prison population was 475 , 000 and increasing at a rate of 35 , 000 per year. Thus the rate of change of n is 35 and n = 475 . Therefore, d n d t = 35 at n = 475 . Since, the average SAT score and how fast, and in what direction is it changing. Thus, the above sentence can be rephrased as: What is the rate of change of S and the value of S . Thus, d S d t = ? and S = ? Consider the relationship equation: S ( n ) = 904 + 1 , 326 ( n − 180 ) 1.325 Substitute 475 for n in above equation to calculate the value of S as: S ( n ) = 904 + 1 , 326 ( 475 − 180 ) 1

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 12.5, Problem 49E

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To calculate: The average SAT score and how fast, and in what direction is it changing where the U.S prison population was 475,000 and increasing at a rate of 35,000 per year.

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Chapter 12.5, Problem 48E

Chapter 12.5, Problem 50E

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The average SAT score and how fast, and in what direction is it changing where the U.S prison population was 475 , 000 and increasing at a rate of 35 , 000 per year.

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To calculate: The average SAT score and how fast, and in what direction is it changing where the U.S prison population was 475,000 and increasing at a rate of 35,000 per year.

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