Question

The present population of a town is 5,50,000. There is an annual increase of 4% in the population. What will be the population after 3 years?

Answer 1

Hint: Consider the present population of the town as ${{P}_{0}}$, annual rate of increase in the population as r% and time after which we need to find the population as t. Now, apply the formula ${{P}_{t}}={{P}_{0}}{{\left( 1+\dfrac{r}{100} \right)}^{t}}$ to calculate the total population after t years. Substitute the given values t = 3 years, r = 4 and ${{P}_{0}}$ = 5,50,000.

Complete step by step solution:
Here we are provided with the present population of a town as 5,50,000 which increases annually at a rate of 4%. We have been asked to calculate the total population after 3 years.
Now, the formula to calculate the population after a certain time interval in years is given as ${{P}_{t}}={{P}_{0}}{{\left( 1+\dfrac{r}{100} \right)}^{t}}$ where ${{P}_{t}}$ is the population after t years, ${{P}_{0}}$ is the present population, t is time interval in years and r is the annual rate of increase. According to the question we have ${{P}_{0}}$ = 5,50,000, t = 3 years and r = 4. So substituting these values in the formula we get,
$\begin{align}
  & \Rightarrow {{P}_{3}}=550000\times {{\left( 1+\dfrac{4}{100} \right)}^{3}} \\
 & \Rightarrow {{P}_{3}}=550000\times {{\left( \dfrac{104}{100} \right)}^{3}} \\
\end{align}$
On simplifying we get,
\[\Rightarrow {{P}_{3}}=618675.2\]
Now, the number of people cannot be in fraction or decimal so we need to round off the above value to the nearest whole number. So we get,
\[\Rightarrow {{P}_{3}}=618675\]
Hence the total population of the town after 3 years will be 6,18,675.

Note: You may note that the formula that we have used to calculate total population is almost similar to the formula used for the calculation of compound interest. So, you can relate both the situations. You can also calculate the answer using a long basic approach. In that case you will have to calculate the population at the end of each year one by one. So there will be three steps to answer which will be somewhat time taking.