Fish enter a lake at a rate modeled by the function E given by ( ) 20 15sin 6 t E t          . Fish leave the lake at a rate modeled by the function L given by 2 0.1 L( ) 4 2 t t   . 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.

The number of fish that enter the lake from midnight (t = 0) to 5 A.M. (t = 5) is 101 fish

Step-by-step explanation:

Given that

Fish enter a lake at a rate modeled by the function E given by E(t) = 20 + 15 sin(πt/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4 + 2^0.1t2. 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)?

Please find the attached file for the solution