Question

The population of a small town is 23,781 and has been continuously declining at a rate of 3.2% each year what is the approximate population of the town in 17 years

Answer 1

same as the car one

A=Pe^(rt)
when it is a decay, make r negative
P=23781 and r=-0.032 and t=17
A=23781e^(-0.032*17)
A=23781e^(-0.554)
A=13803.01
so about 13803 people is the population after 17 years

Answer 2

Explanation:

Given that the population of a small town is 23,781 and has been continuously declining at a rate of 3.2% each year

Continuously declining is given hence we have the population P(t) as

`P(t) = 23781 e^(-0.032t)` where t represents the number of years from initial time.

To find approximate population of the town in 17 years substitute t =17 in the equation

`P(17) = 23781e^(-0.032(17)) \\P(17) = 23781 e^(-0.544)\\=13803.79`

i.e. approximate population of the town in 17 years = 13804