Question

A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t) = (944)3 t/3, where t represents the number ofyears from the time of introduction.What is the tripling-time for this population of deer?

Answer 1

Ok, so

Here we have the function:

`P(t)=944(3)^{(t)/(3)}`

Now we want to find the tripling-time for this population of deer.

If we make t=0, we will find the initial population of deer. This is:

`P(0)=944(3)^{(0)/(3)}=944`

Now, we want to find the time "t" such that this population is the triple.

This is:

`\begin{gathered} 944(3)=944(3)^{(t)/(3)} \\ 2832=944(3)^{(t)/(3)} \\ (2832)/(944)=3^{(t)/(3)} \\ 3=3^{(t)/(3)} \end{gathered}`

We got this exponential equation:

`3=3^{(t)/(3)}`

As the base is the same, we could equal the exponents:

`\begin{gathered} 1=(t)/(3) \\ t=3 \end{gathered}`

Therefore, tripling-time for this population of deer are 3 years.