   Chapter 4.5, Problem 7CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Suppose the average test score in Example 7 was modeled by p =   92.3   −   16.9  ln ( t + 1 ) , 0   ≤ t ≤   48 where t is the time in months. How would the rate at which the average test score was changing after 1 year compare with that of the model in Example 7?

To determine

To calculate: The rate at which the average test score was changing after 1 year if 200 college students, who had taken Spanish during the fall semester of freshman year but did not take subsequent Spanish courses, were tested every 6 months for four years and the average test score is approximated by the function p=92.316.9ln(t+1).

Explanation

Given information:

It is given that 200 college students, who had taken Spanish during the fall semester of freshman year but did not take subsequent Spanish courses, were tested every 6 months for four years and the average test score is approximated by the function p=92.316.9ln(t+1) where (0t48) t is the time in months and graph is:

Formula used:

Let u be a differentiable function of x then, ddx[lnx]=1x,x>0 and ddx(lnu)=1ududx,u>0

Calculation:

Consider that 200 college students, who had taken Spanish during the fall semester of freshman year but did not take subsequent Spanish courses, were tested every 6 months for four years and the average test score is approximated by the function p=92.316.9ln(t+1) where (0t48) t is the time in months

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