Question

Suppose 175 trout are seeded into a lake. Absent constraint, their population will grow by 45% a year. If the lake can sustain a maximum of 3500 trout, use a logistic growth model to estimate the number of trout after 2 years.

Answer 1

Answer with Explanation: Initially 175 trout are seeded into the lake, and the population grows by 45% each year, using the logistic model, after t years, the population would be as follows:

$P\left(t\right)=175\left(1.45\right)^t$

The number of trouts in the lake after two years would be as follows:

$\begin{gathered} P(2)=175(1.45)^{\left(2\right)} \\ P\left(2\right)=175*\left(1.45\right)*\left(1.45\right) \\ P\left(2\right)=367.9375 \end{gathered}$

In conclusion, after two years, the number of trouts in the lake would be close to 368 which is less than the maximum trouts that the lake can support or 3500 trouts.