(4) Suppose a population initially grows, but is then exposed to an environmental toxin that causes the population to go (locally) extinct. One reasonable model for this (with t in months) isP(t)=50t1000-2t22(a) Graph this function. Determine where P(t)=0. These values of t determine the domain of P. What is this domain? Your answer should be an interval of time values: ctd for what numbers c and d?50t50t1000-2t22=050t1000-2t22=021000-2t2=0-1000-2t2-2=-1000-2t22=5002t=+-5002t=0att=-1052t=1052-1052t1052c=-1052,d=1052(b) Find the derivative of P with respect to t. Show steps using the product rule first, then the chain rule.