Chapter 4.4, Problem 51E

Memorizing. In a memory experiment, Alan is able to memorize words at the rate (in words per minute) given by

$m^{\prime }\left(t\right)=-0.009t^2+0.2$.

In the same memory experiment, Bonnie is able to memorize words at the rate given by

$M^{\prime }\left(t\right)=-0.003t^2+0.2t$.

a. How many more words does the person whose memorization rate is higher memorize from $t=0\text{ to }t=10$

(during the first 10 min of the experiment)?

b. Over the first 10 min of the experiment, on average, how many words per minute did Alan memorize?

c. Over the first 10 min of the experiment, on average, how many words per minute did Bonnie memorize?