2019 AP Calculus AB FRQ #1

Fish enter a lake at a rate modeled by the function E given by E(t) = 20 + 15 sin(pi * t /6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4 + 2 ^0.1t ^ 2. Both E(t) and L(t) are measured in fish per hour, and t is measured in hours since midnight (t = 0).
(a) How many fish enter the lake over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5) ? Give your answer to the nearest whole number.
(b) What is the average number of fish that leave the lake per hour over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5) ?
(c) At what time t, for 0 to 8, is the greatest number of fish in the lake? Justify your answer.
(d) Is the rate of change in the number of fish in the lake increasing or decreasing at 5 A.M. (t = 5) ? Explain
your reasoning.
Timestamps
Intro: 00:00
Part a: 00:27
Part b: 01:40
Part c: 02:56
Part d: 07:04