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A town's population increases by $5\%$ each year. If the current population is $10,000$ , what will the population be in $5$ years?

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Exponential growth and decay: word problems

Full solution

Q. A town's population increases by

5\%

each year. If the current population is

10,000

, what will the population be in

5

years?

Identify Population and Growth Rate: Identify the initial population and the annual growth rate. $\newline$ The initial population is $10,000$ and the annual growth rate is $5\%$ .
Convert Growth Rate to Decimal: Convert the percentage growth rate to a decimal to use in calculations. $\newline$ $5\%$ as a decimal is $0.05$ .
Use Exponential Growth Formula: Use the formula for exponential growth to calculate the population after $5$ years. $\newline$ The formula is $P = P_0 \times (1 + r)^t$ , where $P$ is the future population, $P_0$ is the initial population, $r$ is the growth rate, and $t$ is the time in years.
Plug Values into Formula: Plug the values into the formula to calculate the future population. $P = 10,000 \times (1 + 0.05)^5$
Calculate Future Population: Calculate the future population. $\newline$ $P = 10,000 \times (1.05)^5$ $\newline$ $P = 10,000 \times 1.2762815625$ $\newline$ $P = 12,762.815625$
Round Population to Nearest Whole Number: Round the population to the nearest whole number, as population is typically not expressed in fractions. $\newline$ P $\approx$ $12$ , $763$

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