Question

The population of a place is 4,000 in the year 1998. If the population of the same place is 16,000 in the year 2000, then the rate of increase in the population is ___.

• A. 50%
• B. 25%
• C. 75%
• D. 100%

Answer 1

The correct option is D 100%

The rate of increase in population is the increase in population compared to the previous year.

We use the concept of compound interest to find the rate of increase in the population.

A = P × ${[1+\frac{R}{100}]}^n$

where, A = population in the year 2000
= 16,000

P = initial population = population in the year 1998
= 4,000
Time (n) = 2 years

$\therefore$ $16,000=4,000$ × $[1+\frac{R}{100}{]}^2$

$⟹4=[1+\frac{R}{100}{]}^2$

$⟹2=1+\frac{R}{100}$

$⟹1=\frac{R}{100}$

$⟹R=100$