Question

The population of a town is $176400$. It increases annually at the rate of $5\%$ p.a. What will be its population after $2$ years? What was it $2$ years ago?

• A. $194481,159201$
• B. $160000,194480$
• C. $194950,159286$
• D. $194481,160000$

Answer 1

The correct option is D $194481,160000$

$N_0$ - Initial population

$r$ - Rate at which population changes

$n$ - Number of years

Population after $n$ years = $N_{+}=N_0(1+r{)}^n$

Population before $n$ years = $N_{-}=\frac{N_0}{(1+r{)}^n}$

The population after 2 years = $176400(1+0.05{)}^2=194481$

The population before 2 years = $\frac{176400}{(1+0.05{)}^2}=16000$

$\therefore$ The answer is $\left[D\right]$.