Question

Suppose that the population size P(t) of the species can be modeled by the following function, where time t is measured in years

Answer 1

378 individuals

601 individuals

Step-by-step explanation:

We know that the population after t years is described by:

`P(t)=(790)/(1+7e^(-0.31t))`

So, to know the population after 6 years, we need to replace t by 6 and calculate P(t). Then:

`\begin{gathered} P(6)=(790)/(1+7e^(-0.31(6))) \\ P(6)=(790)/(1+7e^(-1.86)) \\ P(6)=(790)/(1+7(0.156)) \\ P(6)=(790)/(1+1.089) \\ P(6)=(790)/(2.089) \\ P(6)=378 \end{gathered}`

In the same way, we can calculate the population after 10 years replacing t by 10. So:

`\begin{gathered} P(10)=(790)/(1+7e^(-0.31(10))) \\ P(10)=(790)/(1+7e^(-3.1)) \\ P(10)=(790)/(1+7(0.045)) \\ P(10)=(790)/(1+0.3153) \\ P(10)=(790)/(1.3153) \\ P(10)=601 \end{gathered}`

Therefore, the answers are:

378 individuals

601 individuals