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A town has a population of 13000 and grows at
2% every year. What will be the population after 12 years, to the nearest whole number?
Answer:

A town has a population of $13000$ and grows at $2 \%$ every year. What will be the population after $12$ years, to the nearest whole number? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. A town has a population of

13000

and grows at

2 \%

every year. What will be the population after

12

years, to the nearest whole number?

\newline

Answer:

Identify Population and Growth Rate: Identify the initial population and the growth rate. $\newline$ The initial population $P_0$ is $13,000$ and the growth rate $r$ is $2\%$ per year.
Convert Growth Rate to Decimal: Convert the growth rate from a percentage to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $r = 2\% = \frac{2}{100} = 0.02$
Determine Number of Years: Determine the number of years ( $t$ ) the population will grow. $\newline$ The population will grow for $12$ years.
Use Exponential Growth Formula: Use the exponential growth formula to calculate the future population. The exponential growth 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.
Substitute Values and Calculate: Substitute the known values into the formula and calculate the future population. $P = 13000 \times (1 + 0.02)^{12}$
Calculate Future Population: Calculate the future population. $\newline$ $P = 13000 \times (1.02)^{12}$ $\newline$ $P \approx 13000 \times 1.26824$ $\newline$ $P \approx 16487.12$
Round to Nearest Whole Number: Round the population to the nearest whole number. $\newline$ The population after $12$ years, rounded to the nearest whole number, is approximately $16,487$ .

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