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A town has a population of 17000 and grows at
3.5% every year. What will be the population after 9 years, to the nearest whole number?
Answer:

A town has a population of $17000$ and grows at $3.5 \%$ every year. What will be the population after $9$ 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

3.5 \%

every year. What will be the population after

9

years, to the nearest whole number?

\newline

Answer:

Identify initial population and growth rate: Identify the initial population and the growth rate. The initial population $P_0$ is $17,000$ and the growth rate $r$ is $3.5\%$ per year.
Convert growth rate to decimal: Convert the percentage growth rate to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $r = 3.5\% = \frac{3.5}{100} = 0.035$
Determine number of years: Determine the number of years ( $t$ ) the population will grow. $\newline$ The population will grow for $t = 9$ years.
Use exponential growth formula: Use the exponential growth formula to calculate the future population. $\newline$ The formula for exponential growth is $P(t) = P_0 \times (1 + r)^t$ . $\newline$ Substitute $P_0 = 17,000$ , $r = 0.035$ , and $t = 9$ into the formula. $\newline$ $P(9) = 17,000 \times (1 + 0.035)^9$
Calculate future population: Calculate the future population. $\newline$ $P(9) = 17,000 \times (1.035)^9$ $\newline$ First, calculate $(1.035)^9$ . $\newline$ $(1.035)^9 \approx 1.374$ $\newline$ Now, multiply this by the initial population. $\newline$ $P(9) \approx 17,000 \times 1.374$ $\newline$ $P(9) \approx 23,358$
Round to nearest whole number: Round the result to the nearest whole number. $\newline$ The population after $9$ years, rounded to the nearest whole number, is approximately $23,358$ .

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