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Since 2010, the town of Fall River has been experiencing a growth in population.
The relationship between the elapsed time,
t, in years, since 2010 and the town's population,
P(t), is modeled by the following function.

P(t)=36,800*2^((t)/( 25))
According to the model, what will the population of Fall River be in 2020 ?
Round your answer, if necessary, to the nearest whole number.
people

Since $2010$ , the town of Fall River has been experiencing a growth in population. $\newline$ The relationship between the elapsed time, $t$ , in years, since $2010$ and the town's population, $P(t)$ , is modeled by the following function. $\newline$ $P(t)=36,800 \cdot 2^{\frac{t}{25}}$ $\newline$ According to the model, what will the population of Fall River be in $2020$ ? $\newline$ Round your answer, if necessary, to the nearest whole number. $\newline$ people

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Compound interest: word problems

Full solution

Q. Since

2010

, the town of Fall River has been experiencing a growth in population.

\newline

The relationship between the elapsed time,

t

, in years, since

2010

and the town's population,

P(t)

, is modeled by the following function.

\newline

P(t)=36,800 \cdot 2^{\frac{t}{25}}

\newline

According to the model, what will the population of Fall River be in

2020

?

\newline

Round your answer, if necessary, to the nearest whole number.

\newline

people

Identify values and formula: Identify the values of $t$ and the formula for $P(t)$ . $\newline$ The formula given is $P(t) = 36,800 \times 2^{(t/25)}$ . Since we want to find the population in $2020$ , we need to calculate the elapsed time since $2010$ .
Calculate elapsed time: Calculate the elapsed time $t$ since $2010$ . $\newline$ $2020 - 2010 = 10$ years $\newline$ So, $t = 10$ .
Substitute value of t: Substitute the value of t into the population model. $\newline$ $P(t) = 36,800 \times 2^{\frac{10}{25}}$
Simplify the exponent: Simplify the exponent. $2^{\frac{10}{25}} = 2^{0.4}$
Calculate $2^{0.4}$ : Calculate $2^{0.4}$ . $\newline$ Using a calculator, we find that $2^{0.4} \approx 1.31950791$ .
Multiply base population: Multiply the base population by the growth factor to find the population in $2020$ . $\newline$ $P(10) = 36,800 \times 1.31950791$ $\newline$ $P(10) \approx 36,800 \times 1.31950791 \approx 48,558.29128$
Round population: Round the population to the nearest whole number. $P(10) \approx 48,558$ people

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