Question

The city of Anville is currently home to 16000 people, and the population has been growing at a continuous rate of 4% per year. The city of Brinker is currently home to 11000 people, and the population has been growing at a continuous rate of 7% per year. In how many years will the populations of the two towns be equal?

Answer 1

Answer

After 13.15 years the population of both towns will become equal.

Step-by-step explanation:

Population of the city Anville is given by using the compound interest formula  

The formula of compound interest

A = p( 1+r/n)^n*t

using this we get

P1 = 16000 (1 +$\frac{0.04}{1}$) ^1*t

Population of the city of Brinker will be

P2 = 11000( 1  + $\frac{0.07}{1}$) ^1*t

now to make equal population in both towns

P1=P2

16000 (1 +$\frac{0.04}{1}$) ^1*t = 11000( 1  + $\frac{0.07}{1}$) ^1*t

$(\frac{1.04}{1.07} )^t = \frac{11}{16}$

t = 13.15 years