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A town has a population of 17000 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 $17000$ 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

17000

and grows at

2 \%

every year. What will be the population after

12

years, to the nearest whole number?

\newline

Answer:

Determine growth type: Determine the type of growth. The town grows at a constant rate of $2\%$ per year, which indicates exponential growth.
Identify initial population and rate: Identify the initial population ( $P_0$ ) and the growth rate ( $r$ ). $\newline$ $P_0 = 17000$ $\newline$ $r = 2\%$ or $0.02$ when expressed as a decimal.
Use exponential growth formula: Use the formula for exponential growth: $P(t) = P_0 \times (1 + r)^t$ , where $P(t)$ is the population at time $t$ , $P_0$ is the initial population, $r$ is the growth rate, and $t$ is the time in years.
Substitute values into formula: Substitute the known values into the formula. $\newline$ $P(12) = 17000 \times (1 + 0.02)^{12}$
Calculate population after $12$ years: Calculate the population after $12$ years. $\newline$ $P(12) = 17000 \times (1.02)^{12}$ $\newline$ $P(12) = 17000 \times 1.26824$ (rounded to $5$ decimal places) $\newline$ $P(12) = 21560.08$
Round result to nearest whole number: Round the result to the nearest whole number. $\newline$ The population after $12$ years is approximately $21560$ .

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