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(D) Let the initial population be $P_0$. The population after $5 	ext{ yr}$ at an annual growth rate of $3 \%$ is given by $P = P_0(1 + \frac{3}{100}

Vedclass · Accepted Answer

$15.9$

Vedclass · Answer

(D) Let the initial population be $P_0$. The population after $5 	ext{ yr}$ at an annual growth rate of $3 \%$ is given by $P = P_0(1 + \frac{3}{100})^5$. The percentage increase is calculated as: $\frac{P - P_0}{P_0} 	imes 100 = [ (1 + 0.03)^5 - 1 ] 	imes 100$ $= [ (1.03)^5 - 1 ] 	imes 100$ Using the approximation $(1.03)^5 \approx 1.15927$,we get: $\approx [1.15927 - 1] 	imes 100 = 15.927 \% \approx 15.9 \%$. Hence,option $D$ is correct.

The population of a city grows at the annual rate of $3 \%$. What percentage increase is expected in $5 \text{ yr}$ (in $\%$)?

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