QUESTION

# The population of a town increases by $5\%$ every year. If the present population is 50000, find its population after 2 years.

Hint: In this question, the present population is given and the rate of increasing population every year is also given. In order to find the population after 2 years, we will use the direct formula as
Population after n years, where r is rate of increasing, ${\text{ = present population}}{\left( {1 + \dfrac{r}{{100}}} \right)^n}$

Given that population is increasing every year by $5\%$
$\therefore r = 5\%$
And the present population is 50,000
We have to find the population after 2 years
As we know that if we have present population, rate of increasing then population after “n” years
Will be given as ${\text{ = present population}}{\left( {1 + \dfrac{r}{{100}}} \right)^n}$
Substitute the value of r, n and present population, we get
Population after 2 years
$= 50000{\left( {1 + \dfrac{5}{{100}}} \right)^2} \\ = 55125 \\$
Hence the population after 2 years is 5515.

Note: In order to solve these types of questions, remember the formulas of exponential growth and exponential decay. After remembering the formulas you are left with finding the values of r, n and present population, you can find the population at any time asked in the question. Questions can be framed for any of the values by giving other values in the question or in the form of conditions. The basic approach to solving the question remains the same.