Question

The population is decreasing at a rate of 3% per year. If the population is 24,400 today, what will the population be in 8 years? Round your answer to the nearest whole number, if necessary.

Answer 1

Exponential Decay Model

The model for the decrease of a population from an initial value Po to a value of P in t years is:

`P=P_o(1-r)^t`

Where r is decreasing rate, expressed in decimal.

We know r = 3% = 0.03

Po = 24,400

t = 8 years

Calculating:

`\begin{gathered} P=24,400(1-0.03)^8 \\ P=24,400\cdot0.97^8 \\ P=24,400\cdot0.783743 \\ P=19,123 \end{gathered}`

The population in 8 years will be 19,123