Question

13. Suppose 275 trout are seeded into a lake. Absent constraint, their population will grow by 35% a year. If the lake can sustain a maximum of 2700 trout, use a logistic growth model to estimate the number of trout after 2 years. trout

Answer 1

Logistic Growth Model

It's commonly used to model population growth in a variety of fields of science.

The formula to calculate the population after a time t is given by:

$P(t)=\frac{P_m}{1+(\frac{P_m-P_o_{}}{P_o})e^{-kt}}$

Where Pm is the maximum value of P, k is the growth rate, Po is the initial value of P, and t is the time.

The values taken from the question are Pm=2700, Po = 275, k=35%=0.35, t=2

Substituting and calculating:

$\begin{gathered} P(2)=\frac{2700}{1+(\frac{2700-275}{2700})e^{-0.35\cdot2}}=\frac{2700}{1+0.8981\cdot e^{-0.7}} \\ P(2)=\frac{2700}{1.446}=1867 \end{gathered}$

The estimated number of trout after 2 years is 1867