Question

A population of a certain species of turtle is 24,000 animals and is decreasing at the rate of 10% per year.Write an equation for y, the population at time t (in years), representing the situation.y =How many turtles are in the population after 9 years?

Answer 1

In this problem, we have an exponential decay function of the form

$y=a(1-r)^t$

where

a=24,000 animals

r=10%=10/100=0.10

substitute given values

$\begin{gathered} y=24,000(1-0.10)^t \\ y=24,000(0.90)^t \end{gathered}$

For t=9 years

substitute in the equation

$\begin{gathered} y=24,000(0.90)^9 \\ y=9,298\text{ turtles} \end{gathered}$