5 c Auto saved at: 19:4 POSSIBLE POINTS: 14.85 An ecology student is studying the repopulation of wild ostriches in Oudtshoorn after a drought. The population growth rate is approximately logistic, so dp dt = KP(1-) where P(t) is the population t years after her study begins. The carrying capacity A is known to be 200 000 ostriches, since this was the population before the drought. Initially, the student finds that there are 25 000 ostriches. After two years she finds there are 31 200 ostriches. a Solve the differential equation, and use the population P(0) and P(2) to find the population P(t) after t years. b Estimate the ostrich population after 5 years. c Find the time at which the population growth rate is a maximum