Question

The population of a certain inner-city area is estimated to be declining according to the model P(t)=385,000e−0.022t, where t is the number of years from the present. What does this model predict the population will be in 9 years? Round to the nearest person.

Answer 1

Answer:

This model predicts that population will be 315,842 in 9 years.

Step-by-step explanation:

Let the population of the city be represented by the function $p(t) = 385,000\cdot e^{-0.022\cdot t}$, where $t$ is the number of years from the present. The negative exponent means that such city is expected to experiment a sustained decrease. The predicted population in 9 years is determined by evaluating the function at $t = 9$:

$p(9) = 385,000\cdot e^{-0.022\cdot (9)}$

$p(9) = 315,842.394$

$p(9) = 315,842$

This model predicts that population will be 315,842 in 9 years.