Chapter 4.4, Problem 52E

Results of studying. Celia’s score on a test, $s\left(t\right)$, after t hours of studying, is given by

$s\left(t\right)=t^2,0\le t\le 10$,

Dan’s score on the same test is given by

$S\left(t\right)=10t,0\le t\le 10$,

where $S\left(t\right)$

is his score after t hours of studying.

a. For $0<t<10$, who will have the higher test score?

b. Find the average value of $s\left(t\right)$

over $\left[7,10\right]$, and explain what it represents.

c. Find the average value of $S\left(t\right)$

over $\left[6,10\right]$, and explain what it represents.

d. Assuming that both students have the same study habits and are equally likely to study for any number of hours, t, in [0, 10][0, 10], on average, how far apart will their test scores be?