Question

If the current population of Chennai city is 3888180 and the average rate of population growth in Chennai city is 10 % p.a., what can city planners expect the population of Chennai city to be in 10 years?

Answer 1

Hint: The total population of a place with current population P, growth rate R % p.a. and the number of years N is given as \[P{\left( {1 + \dfrac{R}{{100}}} \right)^N}\]. Use this to find the population of Chennai city in 10 years.

Complete step-by-step solution -
The growth in the population of a city is just like the compound interest of a sum. It includes the growth of the accumulated people along with the initial population for the given period and given rate.
The final population of a place with current population P, growth rate R % p.a. and the number of years N is given as follows:
\[P' = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}............(1)\]
In this question, it is given that the initial population of the Chennai city is 3888180. Hence, we have:
P = 3888180
The average population growth rate is given as 10 % p.a. Hence, we have:
R = 10
The number of years considered is 10 years. Hence, we have:
N = 10
Using equation (1), we calculate the population of Chennai city after 10 years.
\[P' = 3888180{\left( {1 + \dfrac{{10}}{{100}}} \right)^{10}}\]
Simplifying, we have:
\[P' = 3888180{\left( {1.1} \right)^{10}}\]
The value of \[{\left( {1.1} \right)^{10}}\] is equal to 2.5937 approximately, then, we have:
\[P' = 3888180 \times 2.5937\]
\[P' = 10084772\]
Hence, the population of Chennai city after 10 years will be 10084772.

Note: We may think that this problem is similar to simple interest but remember that the population accumulates each year and for the next year, the accumulated population is also included. Hence, We must use compound interest formula and not simple interest formula.