Question

The population of a suburb is 16000. Find the rate of increase in the population if the population after two years is 17640.

Answer 1

Let the rate of increase in the population is r
we know, population increases geometrical progression so, we have to use $\textbf{compound interest}$ formula

Given, P = 16,000
time period , n = 2
population after 2 yrs , A = 17640
use formula $A=P\left(\begin{array}{c}1+\frac{r}{100}\end{array}\right)^n$
so, 17640 = 16000(1 + r/100)²
=> 17640/16000 = (1 + r/100)²
=> 1764/1600 = (1 + r/100)²
=> 441/400 = (1 + r/100)²
taking square root both sides,
=> 21/20 = 1 + r/100
=> 21/20 - 1 = r/100
=> 1/20 × 100 = r
r = 5 %

Answer 2

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