Dom, the manager of a fishery, determines that t weeks after 300 fish of a particular species are released into a pond, the average weight of an individual fish (in pounds) for the first 10 weeks will be w(t) = 3 + t − 0.05t² Dom further determines that the proportion of the fish that are still alive after t weeks is given by

a. The expected yield Y(t) of the fish after t weeks is the total weight of the fish that are still alive. Express Y(t) in terms of w(t) and p(t), and sketch the graph of Y(t) for 0 ≤ t ≤ 10.

b. When should Dom expect the yield Y(t) to be maximized? What is the maximum yield?

Transcribed Image Text:

p(t) 31 31 + t