Mathematics: A species of animal is discovered on an island. Suppose that the population size P(t) of the species can be modeled by the following function, where time t is measured in years. P(t) =800/1+ 3e^-0.29t. Find the initial population size of the species and the population size after 10 years. Round your answers to the nearest whole number as necessary.

I believe the monkey would be 40ft off the groundStep-by-step explanation:...

A species of animal is discovered on an island.

Perdikaris

17.03.2022

The initial population is 200

The population after 10 years is 687

Step-by-step explanation:

Given

$P(t) =\frac{800}{1+ 3e^{-0.29t.}}$

Solving (a): The initial population

Here:

t = 0

Substitute 0 for t in P(t)

$P(0) =\frac{800}{1+ 3e^{-0.29*0}}$

$P(0) =\frac{800}{1+ 3e^{0}}$

$P(0) =\frac{800}{1+ 3*1}$

$P(0) =\frac{800}{1+ 3}$

$P(0) =\frac{800}{4}$

P(0) =200

The initial population is 200

Solving (b): Population after 10 years.

Here

t = 10

Substitute 10 for t in P(t)

$P(10) =\frac{800}{1+ 3e^{-0.29*10}}$

$P(10) =\frac{800}{1+ 3e^{-2.9}}$

$P(10) =\frac{800}{1+ 3*0.055}$

$P(10) =\frac{800}{1+ 0.165}$

$P(10) =\frac{800}{1.165}$

P(10) =687 -- approximated.

The population after 10 years is 687

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