If P0 > c (which implies that

Question

−1 < a < 0),
then the logistics function
P(t) =
c
1 + ae−bt
decreases as t increases. Biologists often use this type of logistic function to model populations that decrease over time. See the following figure. Apply this information to the exercise.

A biologist finds that the fish population in a small lake can be closely modeled by the logistic function
P(t) =
3000
1 + (−0.6667)e−0.05t
where t is the time, in years, since the lake was first stocked with fish.

(a) What was the fish population when the lake was first stocked with fish?


(b) According to the logistic model, what will the fish population approach in the long-term future?

Answer 1

(b)3000