The population of a town increases 4 % annual | vedclass

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Question

(D) Let the initial population of the town be $P$.The net annual growth rate of the population is $4 \% - 0.5 \% = 3.5 \%$.The population after $3$ ye

Vedclass · Accepted Answer

$10.8$

Vedclass · Answer

(D) Let the initial population of the town be $P$.The net annual growth rate of the population is $4 \% - 0.5 \% = 3.5 \%$.The population after $3$ years is given by the formula $A = P(1 + r/100)^n$,where $r = 3.5$ and $n = 3$.Population after $3$ years $= P(1 + 3.5/100)^3 = P(1 + 0.035)^3 = P(1.035)^3$.Calculating $(1.035)^3 = 1.035 	imes 1.035 	imes 1.035 \approx 1.108717875$.The increase in population is $P(1.108717875) - P = 0.108717875P$.The percentage increase is $(0.108717875P / P) 	imes 100 = 10.8717875 \%$.Rounding to one decimal place,the increase is approximately $10.8 \%$.

The population of a town increases $4 \%$ annually but is decreased by emigration annually to the extent of $(1/2) \%$. What will be the increase per cent in $3$ years?

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