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Suppose 225 trout are seeded into a lake. Absent constraint, their population will grow by 25% a year. If the lake can sustain a maximum of 3500 trout, use a logistic growth model to estimate the number of trout after 5 years. trout

Suppose 225 trout are seeded into a lake Absent constraint their population will grow by 25 a year If the lake can sustain a maximum of 3500 trout use a logisti class=

Respuesta :

It is known that the population growth model is given by:

[tex]P=P_0e^{kt}[/tex]

Initial population is 225 so P0=225 so it follows:

[tex]P=225e^{kt}[/tex]

Each year the population will increase by 25% so it follows:

[tex]\begin{gathered} P_0+0.25P_0=225e^k \\ e^k=\frac{5}{4} \\ k\ln e=\ln (\frac{5}{4}) \\ k\approx0.2231 \end{gathered}[/tex]

So the population function is:

[tex]P=225e^{0.2231t}[/tex]

The population in 5 years is given by:

[tex]P=225e^{0.2231\times5}\approx686.4960025[/tex]

Hence the population of trout will be 686.4960025 after 5 years which can be rounded to 687.

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