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Question
Three years ago, the population of a town was 50000. If the annual increase during three successive years be at the rate of 4%, 5% and 3% respectively, find the present population.
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Solution
Here,
P = Initial population = 50, 000
\[ R_1 = 4 % \]
\[ R_2 = 5 % \]
\[ R_3 = 3 % \]
n = Number of years = 3
∴ Population after three years = P \[\left( 1 + \frac{R_1}{100} \right)\left( 1 + \frac{R_2}{100} \right)\left( 1 + \frac{R_3}{100} \right)\]
\[ = 50, 000\left( 1 + \frac{4}{100} \right)\left( 1 + \frac{5}{100} \right)\left( 1 + \frac{3}{100} \right)\]
\[ = 50, 000\left( 1 . 04 \right)\left( 1 . 05 \right)\left( 1 . 03 \right)\]
\[ = 56, 238\]
Hence, the population after three years is 56, 238.
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