The data in the table in Fig. 2.1.7 are given for a certain population P(t) that satisfies the logistic equation in (3).

(a) What is the limiting population M? (Suggestion: Use the approximation

with h = 1 to estimate the values of P'(t) when P = 25.00 and when P = 47.54. Then substitute these values in the logistic equation and solve for k and M.)

(b) Use the values of k and M found in part (a) to determine when P = 75. (Suggestion: Take t = 0 to correspond to the year 1965.)

P' (t) P(t + h) - P(t-h) 2h