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A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1000 animals and that the growth of the herd will follow the logistic curve P=1000/1+9e^-0.165tWhat is the population after 5 months

Respuesta :

Given:

The growth of the herd will be modelled by the equation.

[tex]P=\frac{1000}{1+9e^{-0.165t}}[/tex]

Where P = Population of the herd

t = time in months

Required:

To find the population after t months.

Explanation:

Substitute t= 5 in the given equation.

[tex]\begin{gathered} P=\frac{1000}{1+9e^{-0.165(5)}} \\ P=\frac{1000}{1+9e^{-0.825}} \end{gathered}[/tex][tex]\begin{gathered} P=\frac{1000}{1+9(0.4382)} \\ P=\frac{1000}{1+9(0.4382)} \\ P=\frac{1000}{1+3.9438} \\ P=\frac{1000}{4.9438} \\ P=202.273 \\ P\approx202 \end{gathered}[/tex]

Final Answer:

The population after 5 months is 202 animals expected.