Question

The population of a wildlife habitat is modeled by the equation LaTeX: p\left(t\right)=\frac{360}{1\:\:+\:\:6.2e^{-0.35t}} p ( t ) = 360 1 + 6.2 e − 0.35 t , where t is given in years. How many animals were originally transported to the habitat?

Answer 1

50 animals.

Explanation:

We have been given that the population of a wildlife habitat is modeled by the equation
`p(t)=(360)/(1+6.2e^(-0.35t))`, where t is given in years. We are asked to find the the number of animals originally transported to the habitat.

To find the the number of animals originally transported to the habitat, we will substitute
`t=0` in our given equation as:

`p(0)=(360)/(1+6.2e^(-0.35(0)))`

`p(0)=(360)/(1+6.2e^(0))`

`p(0)=(360)/(1+6.2(1))`

`p(0)=(360)/(7.2)`

`p(0)=50`

Therefore, 50 animals were originally transported to the habitat.