Question

The population of Town A increases by 5% every year. Its current population is 700,000. Town B, which currently has 550,000 residents, increases by 6.5% each year. If the growth of each town continues to increase at the current rate, what is the difference in the populations of Town A and Town B at the end of 5 years?

Answer 1

Town A has 139,849 more residents than Town B after 5 years, compared to 150,000 more at the beginning of the 5 years.

Explanation:

Town A

y = 700000(1.05)ˣ

Town B

y = 550000(1.065)ˣ

After 5 years:

Town A has 893,397.0938, rounded to 893,397 residents.

Town B has 753,547.6649, rounded to 753,548 residents.

Town A has 139,849 more residents than Town B after 5 years, compared to 150,000 more at the beginning of the 5 years.

Answer 2

Town A has 139,849 more residents than Town B.

Explanation:

The population of each town is increasing exponentially.

A = P( 1 + r/n)nt

Town A: 700000(1 + 0.05)5 = 893,397 residents

Town B: 550,000(1 + 0.065)5 = 753,548

Difference: 893,397 − 753,548 = 139,849