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A town has a population of 36,500 and grows at a rate of
6.4% every year. Which equation represents the town's population after 5 years?

P=36,500(1+0.064)

P=36,500(1-0.064)^(5)

P=36,500(0.936)^(5)

P=36,500(1+0.064)^(5)

A town has a population of $36$ , $500$ and grows at a rate of $6.4 \%$ every year. Which equation represents the town's population after $5$ years? $\newline$ $P=36,500(1+0.064)$ $\newline$ $P=36,500(1-0.064)^{5}$ $\newline$ $P=36,500(0.936)^{5}$ $\newline$ $P=36,500(1+0.064)^{5}$

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Write exponential functions: word problems

Full solution

Q. A town has a population of

36

,

500

and grows at a rate of

6.4 \%

every year. Which equation represents the town's population after

5

years?

\newline

P=36,500(1+0.064)

\newline

P=36,500(1-0.064)^{5}

\newline

P=36,500(0.936)^{5}

\newline

P=36,500(1+0.064)^{5}

Rephrase the Question: First, let's rephrase the ＂What is the equation that represents the town's population after $5$ years, given an initial population of $36,500$ and an annual growth rate of $6.4\%$ ?＂
Identify Initial Population and Growth Rate: Identify the initial population $P_0$ and the growth rate $r$ . The initial population is given as $36,500$ , and the growth rate is $6.4\%$ , which can be expressed as a decimal by dividing by $100$ : $r = \frac{6.4}{100} = 0.064$ .
Determine Growth Factor: Determine the growth factor $b$ . The growth factor is $1$ plus the growth rate, so $b = 1 + r = 1 + 0.064 = 1.064$ .
Write Exponential Growth Equation: Write the exponential growth equation. The general form of an exponential growth equation is $P = P_0 \times b^t$ , where $P$ is the population after time $t$ , $P_0$ is the initial population, $b$ is the growth factor, and $t$ is the time in years. In this case, $t = 5$ years.
Substitute Known Values: Substitute the known values into the equation to get the specific equation for this problem: $P = 36,500 \times (1.064)^5$ .

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