Question

Suppose a city with population 200,000 has been growing at a rate of 7% per year. If this rate continues, find the population of this city in 18 years

Answer 1

In 18 years time, the population of the city is approximately 705,084

Explanation:

From the given information, the initial population is

`P_0=200000`

The growth rate is 7% or r=0.07.

For a population with a continuous growth rate, the equation is that models it is:

`P(t)=P_0 {(e)}^(rt)`

`P(t)=200000 {(e)}^(0.07t)`

To find the find the population after 18 years, we substitute t=18 into:

`P(18) = 200000{(e)}^(18* 0.07)`

`P(18)=705084.3`