The problem states that the population of a town increases by 2% of the initial population every year. We need to find out the number of years it takes for the total increase in population to be 40%.




One way to solve this problem is by using the formula for compound interest. The formula is:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the initial amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.


If the population increases by 40%, the final amount will be 1.4 times the initial amount. So, we can write:

1.4P = P(1 + r/100)^t

Simplifying this equation, we get:

1.4 = (1 + r/100)^t

Taking the natural logarithm of both sides, we get:

ln(1.4) = t ln(1 + r/100)

Solving for t, we get:

t = ln(1.4) / ln(1 + r/100)


We know that the population increases by 2% every year. So, we can substitute r = 2 in the above formula:

t = ln(1.4) / ln(1 + 2/100)
t = ln(1.4) / ln(1.02)
t ≈ 21.97

Therefore, it will take approximately 22 years for the total increase in population to be 40%.


The population of a town increases by 2% of the initial population every year. To find the number of years it takes for the total increase in population to be 40%, we can use the formula for compound interest. By substituting the value of r as 2 (as the population increases by 2% every year), we get the answer as approximately 22 years.