Question

Suppose 125 trout are seeded into a lake. Absent constraint, their population will grow by 75% a year. If the lake can sustain a maximum of 3800 trout, use a logistic growth model to estimate the number of trout after 3 years.

Answer 1

Answer: 125 trout fish would grow at the rate of 75% in no constrain scenario, the model that predicts the fish after t years is as follows:

$T(t)=125(1.75)^t\rightarrow(1)$

Therefore after 3 years, the population would be, using equation (1):

$\begin{gathered} T(t)=125(1.75)^{t} \\ T(3)=125(1.75)^3 \\ T(3)=125(1.75)(1.75)(1.75) \\ T(3)=669.921875 \\ T(3)\approx670 \end{gathered}$