An organism has size w at time t for positive constants a b

Question

Question: An organism has size W at time t. For positive constants A, b, and c, the Gompertz growth function gives

W = Ae^{eb - ct}, t ≥ 0

(a) Find the intercepts and asymptotes.

(b) Find the critical points and inflection points.

(c) Graph W for various values of A, b, and c.

(d) A certain organism grows fastest when it is about 1/3 of its final size. Would the Gompertz growth function be useful in modeling its growth? Explain.