Question

A town has a population of 7000 and grows at 3% every year. To the nearest year, how long will it be until the population will reach 12400?

Answer 1

Answer: It takes almost 19 years to reach the population of 12400.

Explanation:

Since we have given that

Initial Population = 7000

Rate of growth = 3% every year

Final population = 12400

We need to find the number of years.

As we know the formula for "Compound Interest":

`A=P(1+(r)/(100))^n\\\\12400=7000(1+(3)/(100))^n\\\\(12400)/(7000)=(103)/(100)^n\\\\(124)/(70)={1.03}^n\\\\1.771=1.03^n\\\\\text{ Taking logarithms on both the sides}\\\\\log 1.77=n\log 1.03\\\\n=(\log 1.77)/(\log 1.03)\\\\n=19.31\\\\n=19\ yrs`

Hence, It takes almost 19 years to reach the population of 12400.