Need help with a b c please show work. Thanks

Life science. A scientist studies the population P of deer on an island, and determines that it is best modeled 550 by P(t) = where t is in months since 1 + 27e-0.033t' observations began. [3.8] a) After how many months is the population increasing the fastest? b) What is the rate of change in the population at the time found in part (a)? c) Why might the scientist have chosen the logistic function to model the population