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.

Step-by-step 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":

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

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