Question

ite contains an estimated 80,000 fish, with natural population growth Year. The annual catch by local fisherman depletes this population Problem(4)[10 pts.] A local fishing site contains an es rate of 10% per year. The annual catch by by the amount of 7,000 fish per year. (a) Set up a differential equation that models the gr ering the effect of fishing. State clearly as you can what phy the fish population model is based on. (b) Using qualitative analysis, sketch graph of population how this graph is obtained. (c) Based on your answer in (b) can current an “your answer in (b) can current annual catch be sustained indefinitely! Confirm the result by finding the exact solution of the equation. erential equation that models the growth of fish population, consid- clearly as you can what physical assumptions about sketch graph of population vs. time. Explain briefly

Answer 1

Given ahing Aik conteina 80,000 fiah Populo hion grewh vate pev year 107. cateh by local faherman by 7,000 pen yeav be the Populaim f fiohon infinh he gvowth ate bt De cveaned by Fo00 fishes yeav 10 Y: 0 dYP000 o. 1P-7000 dt tP 7000) P 70000 integ vating boh ides

Inl p.0,0 (0.1t) p-70,00 :A P 0,000 P80,000 80,000 A +70,000 A 10,000 10,000 70, 000 10,000 70, 000 Th g vaph populat tine