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Chloe has a collection of vintage action figures that is worth
$310. If the collection appreciates at a rate of
15% per year, which equation represents the value of the collection after 5 years?

V=310(1.15)^(5)

V=310(1+0.15)

V=310(1-0.15)^(5)

V=310(0.85)^(5)

Chloe has a collection of vintage action figures that is worth $\$ 310$ . If the collection appreciates at a rate of $15 \%$ per year, which equation represents the value of the collection after $5$ years? $\newline$ $V=310(1.15)^{5}$ $\newline$ $V=310(1+0.15)$ $\newline$ $V=310(1-0.15)^{5}$ $\newline$ $V=310(0.85)^{5}$

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Write exponential functions: word problems

Full solution

Q. Chloe has a collection of vintage action figures that is worth

\$ 310

. If the collection appreciates at a rate of

15 \%

per year, which equation represents the value of the collection after

5

years?

\newline

V=310(1.15)^{5}

\newline

V=310(1+0.15)

\newline

V=310(1-0.15)^{5}

\newline

V=310(0.85)^{5}

Question Prompt: Question prompt: Which equation represents the value of Chloe's vintage action figure collection after $5$ years, given a $15\%$ annual appreciation rate?
Identify Values: Identify the initial value $a$ and the growth rate $r$ . The initial value of the collection is $\$310$ , and the annual appreciation rate is $15\%$ , which can be expressed as a decimal $0.15$ .
Convert Rate to Factor: Convert the appreciation rate to a growth factor ( $b$ ). $\newline$ The growth factor is found by adding $1$ to the appreciation rate expressed as a decimal. $\newline$ $b = 1 + r$ $\newline$ $b = 1 + 0.15$ $\newline$ $b = 1.15$
Write Exponential Equation: Write the exponential growth equation using the initial value and the growth factor. $\newline$ The general form of the exponential growth equation is $V = a(b)^t$ , where $V$ is the final value, $a$ is the initial value, $b$ is the growth factor, and $t$ is the time in years. $\newline$ Substitute $\$310$ for 'a', $1.15$ for 'b', and $5$ for 't'. $\newline$ $V = 310(1.15)^5$

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