Fish enter a lake at a rate modeled by the function E given by E(1) = 20 + 15 sin ( ). Fish leave the lake at a rate modeled by the function L given by L(1) = 4 + 20.15. Both E(1) and L(:) are measured in fish per hour, and t is measured in hours since midnight (1 = 0). (a) How many fish enter the lake over the 5-hour period from midnight (1 = 0) to 5 A.M. (1 = 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 (1 = 0) to 5 A.M. (1 = 5) ? (c) At what time t, for 0 S / 5 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. (1 = 5) ? Explain your reasoning