Question

Suppose 275 trout are seeded into a lake. Absent constraint their population will grow by 75% 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

Answer 1

Answer: 1729 trout.

Explanation:

We can use the logistic growth model to estimate the number of trout after 2 years:

N(t) = K / (1 + (K/N0 - 1) * e^(-rt))

where:

N(t) is the number of trout at time t

K is the carrying capacity of the lake (2700 trout)

N0 is the initial population (275 trout)

r is the growth rate (75% or 0.75, per year)

e is the base of the natural logarithm, approximately equal to 2.71828

To estimate the number of trout after 2 years, we can plug in t = 2 and solve for N(t):

N(2) = 2700 / (1 + (2700/275 - 1) * e^(-0.75*2))

N(2) = 2700 / (1 + 8.8 * e^(-1.5))

N(2) ≈ 1728.7

Therefore, we can estimate that the number of trout after 2 years will be approximately 1729 trout.