Question

The population of a certain inner-city area is estimated to be declining according to the model P(t)=466,000e^(−0.018t), where t is the number of years from the present. What does this model predict the population will be in 12 years? Round to the nearest person.

Answer 1

To find the prediction of the model we need to substitute t = 12 into the equation as follows:

$\begin{gathered} P(t)=466,000\cdot e^{-0.018\cdot12} \\ P(t)=466,000\cdot e^{-0.216} \\ P(t)=375,473 \end{gathered}$

According to this model, the population will be 375,473 people.