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(t) = −0.2t2 + 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).
Because
g(t)
is positive, the students' receptivity is increasing.
Because
g(t)
is positive, the students' receptivity is decreasing.
Because
g'(t)
is negative, the students' receptivity is decreasing.
Because
g'(t)
is negative, the students' receptivity is increasing.