Question

What is the doubling timefor this population of alligators ?

Answer 1

Answer:

3 years

Explanations:

The given function representing the population of alligators is:

`P(t)\text{ = (}319)2^{(t)/(3)}`

Find the intial population at t = 0

`\begin{gathered} P(0)\text{ = 319 }*2^0 \\ P(0)\text{ = 319 }*\text{ 1} \\ P(0)\text{ }=\text{ 319} \end{gathered}`

The population will double when:

P(t) = 319 x 2

P(t) = 638

The doubling time is the value of t at which P(t) = 638

`\begin{gathered} P(t)\text{ = 319 }*2^{(t)/(3)} \\ 638\text{ = 319 }*2^{(t)/(3)} \\ (638)/(319)=2^{(t)/(3)} \\ 2\text{ }=2^{(t)/(3)} \\ 2^1=2^{(t)/(3)} \\ 1\text{ = }(t)/(3) \\ t\text{ = 3} \end{gathered}`

The population will double after 3 years.

Therefore, the doubling-time for this population of alligators is 3 years