Chapter 9.3, Problem 52E

Receptivity In learning theory, receptivity is defined as the ability of students to understand a complex concept. Receptivity is highest when the topic is introduced and tends to decrease as time passes in a lecture. Suppose that the receptivity of a group of students in a mathematics class is given by

$g\left(t\right)=-02t^2+3.1t+32$ where t is minutes after the lecture begins.

(a) At what rate is receptivity changing 10 minutes after the lecture begins?

(b) Write a sentence that explains the meaning of your answer in part (a).