Question

A population of penguins is given by Pt=P0⋅3t5 where t is the time in years, t≥0. How long does it take for the population to triple its size?

Answer 1

5 years

Explanation:

If the population of penguins is given by the function:

`P(t)=P_0\cdot 3^(t/5)`

Initial Size =
`P_0`

Triple its Initial Size, P(t)=
`3P_0`

Therefore:

`3P_0=P_0\cdot 3^(t/5)\\$Divide both sides by P_0\\3=3^(t/5)\\$Since they have the same base\\1=t/5\\Cross multiply\\t=5`

It therefore takes 5 years for the penguin population to triple in size.