The rate of change of a population P of an environment is determined by the logistic formula
dP/dt =0.04P(1-P/20000)
where t is in years since the beginning of 2015. So P (1) is the population at the beginning of 2016. Suppose P (0) = 1000.
(a) Calculate P′(0)
(b) Use the number from the previous part to estimate the population in the middle of 2015. That is, estimate P (0.5)
(c) What assumption is made in the computation in the previous part? Use the formula given for P ′ to see whether or not the assumption is true, to within 1%