Fish in a lake increases continuously at a rate of 20% per year. Fishing removes about 300 fish per year. The population starts at 2500 fish. 1. What is the equation where P is the population of fish after t years and dedt is how fast the population grows each year. 2. We will be approximating the fish population with polynomials. Let P(tlI =a0+a1t+a2t2+a3t3+... a. What is P{t) at t = 0 in terms of the polynomial and in terms of the problem. b. Find dP/dt where P(t) =a0+a1t+a2t2+a3t3+... Substitute both dP/dt and P{t) into your equation from #1. You will have an infinite sum on both sides. c. Find the constant term on both sides. Set them equal. What new coefficient do we know? Use this to find the linear approximation. d. Find the coefficient of t on both sides of your equation from (bi. These two coefficients should be equal. What new coefficient of P{t} do we get? Use this to find the quadratic approximation. e. Find the coefficient of t2 on both sides of your equation from (b) . These two coefficients should be equal. What new coefficient of P{t} do we get? Use this to find the cubic approximation. f. Continue the process of finding higher degree approximations for P(t) until you have one that is accurate up to the 10005 place at 2 years and explain how you know it is accurate