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A town has a population of 14000 and grows at
3% every year. What will be the population after 14 years, to the nearest whole number?
Answer:

A town has a population of $14000$ and grows at $3 \%$ every year. What will be the population after $14$ 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

14000

and grows at

3 \%

every year. What will be the population after

14

years, to the nearest whole number?

\newline

Answer:

Identify Population and Rate: Identify the initial population and the growth rate. $\newline$ The initial population $P_0$ is $14,000$ and the growth rate $r$ is $3\%$ 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 $100$ . $\newline$ $r = 3\% = \frac{3}{100} = 0.03$
Determine Number of Years: Determine the number of years ( $t$ ) the population will grow. $\newline$ The population will grow for $t = 14$ 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 $P_0 = 14,000$ , $r = 0.03$ , and $t = 14$ into the formula. $\newline$ $P(14) = 14,000 \times (1 + 0.03)^{14}$
Calculate Future Population: Calculate the future population. $\newline$ $P(14) = 14,000 \times (1.03)^{14}$ $\newline$ $P(14) = 14,000 \times 1.03^{14}$ $\newline$ $P(14) \approx 14,000 \times 1.503630$ $\newline$ $P(14) \approx 21,050.82$
Round Population to Nearest: Round the population to the nearest whole number. $\newline$ The population after $14$ years, rounded to the nearest whole number, is approximately $21,051$ .

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