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Richmond County has a population of $850,000$ people, which increases by $10\%$ every year due to a growing tech industry. What will the population be in $2$ years? If necessary, round your answer to the nearest whole number. $\newline$ ____ people $\newline$

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Exponential growth and decay: word problems

Full solution

Q. Richmond County has a population of

850,000

people, which increases by

10\%

every year due to a growing tech industry. What will the population be in

2

years? If necessary, round your answer to the nearest whole number.

\newline

____ people

\newline

Identify Population and Growth Rate: Identify the initial population and the rate of growth. The initial population $P_0$ is $850,000$ people, and the growth rate $r$ is $10\%$ 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 $100$ . $\newline$ $r = 10\% = \frac{10}{100} = 0.10$
Determine Number of Years: Determine the number of years ( $t$ ) over which the population grows. $\newline$ The population is growing over a period of $2$ years. $\newline$ $t = 2$
Use Exponential Growth Formula: Use the formula for exponential growth to calculate the future population. The formula for exponential growth is $P(t) = P_0 \times (1 + r)^t$ , 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.
Calculate Future Population: Substitute the known values into the formula and calculate the population after $2$ years. $\newline$ $P(2) = 850,000 \times (1 + 0.10)^2$ $\newline$ $P(2) = 850,000 \times (1.10)^2$ $\newline$ $P(2) = 850,000 \times 1.21$ $\newline$ $P(2) = 1,028,500$
Round Answer if Necessary: Round the answer to the nearest whole number if necessary. $\newline$ The calculated population is already a whole number, so no rounding is necessary.

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