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Question
The population of a city is 125000. If the annual birth rate and death rate are 5.5% and 3.5% respectively, calculate the population of city after 3 years.
Solution
Here, P = Initial population = 1,25,000
Annual birth rate = `"R"_1` = 5.5 %
Annual death rate = `"R"_2` = 3.5 %
Net growth rate, R = \[\left( R_1 - R_2 \right) = 5.5 - 3.5 = 2 %\]
n = Number of years = 3
∴ Population after three years = P \[ \left( 1 + \frac{R}{100} \right)^n \]
\[=1,25,000\left(1+\frac{2}{100}\right)^3 \]
\[=1,25,000\times\left(1.02\right)^3\]
\[= 1,32,651\]
Hence, the population after three years will be 1,32,651.
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