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

Answer:

5 years

Step-by-step 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.