Question

In 2000 the population of a small village was 2,400. With an annual growth rate of approximately 1.68%, compounded continuously, what will the population be in 2020 according to the exponential growth function?

Answer 1

`3,358\ people`

Explanation:

The formula to calculate the exponential growth function is equal to

`f(x)=P(e)^(rx)`

where

f(x) is the population

P is the population in the year 2000

r is the rate in decimal

x is number of years since 2000

e is the mathematical constant number

we have

`x=2020-2000=20\ years\\ P=2,400\\ r=0.0168`

substitute in the formula above

`f(x)=2,400(e)^(0.0168*20)`

`f(x)=3,358\ people`