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A town has a population of 19000 and grows at
4.5% every year. What will be the population after 9 years, to the nearest whole number?
Answer:

A town has a population of $19000$ and grows at $4.5 \%$ 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

19000

and grows at

4.5 \%

every year. What will be the population after

9

years, to the nearest whole number?

\newline

Answer:

Identify Population and Growth Rate: Identify the initial population and the growth rate. The initial population $P_0$ is $19,000$ , and the growth rate $r$ is $4.5\%$ 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 $100$ . $\newline$ $r = 4.5\% = \frac{4.5}{100} = 0.045$
Determine Number of Years: Determine the number of years ( $t$ ) the population will grow. The population will grow for $t = 9$ years.
Use Exponential Growth Formula: Use the exponential growth formula to calculate the future population. $\newline$ The exponential growth formula is $P(t) = P_0 \times (1 + r)^t$ , where $P(t)$ is the population after $t$ years.
Substitute Values and Calculate: Substitute the known values into the formula and calculate the future population. $\newline$ $P(9) = 19000 \times (1 + 0.045)^9$
Calculate Population After $9$ Years: Calculate the population after $9$ years. $\newline$ $P(9) = 19000 \times (1.045)^9$ $\newline$ $P(9) = 19000 \times 1.453439676$ $\newline$ $P(9) \approx 27625.45404$
Round Population to Nearest Whole Number: Round the population to the nearest whole number. $\newline$ The population after $9$ years, rounded to the nearest whole number, is approximately $27625$ .

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