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A new car is purchased for 23,700 dollars. The value of the car depreciates at a rate of
2% per year. Which equation represents the value of the car after 2 years?

V=23,700(1-0.02)^(2)

V=23,700(1+0.02)^(2)

V=23,700(0.8)^(2)

V=23,700(1.02)^(2)

A new car is purchased for $23$ , $700$ dollars. The value of the car depreciates at a rate of $2 \%$ per year. Which equation represents the value of the car after $2$ years? $\newline$ $V=23,700(1-0.02)^{2}$ $\newline$ $V=23,700(1+0.02)^{2}$ $\newline$ $V=23,700(0.8)^{2}$ $\newline$ $V=23,700(1.02)^{2}$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. A new car is purchased for

23

,

700

dollars. The value of the car depreciates at a rate of

2 \%

per year. Which equation represents the value of the car after

2

years?

\newline

V=23,700(1-0.02)^{2}

\newline

V=23,700(1+0.02)^{2}

\newline

V=23,700(0.8)^{2}

\newline

V=23,700(1.02)^{2}

Identify values: Identify the initial value of the car and the annual depreciation rate. $\newline$ Initial value $P$ = $\$23,700$ $\newline$ Annual depreciation rate $r$ = $2\%$ or $0.02$
Calculate depreciation factor: Understand that depreciation means the value decreases over time. Therefore, we need to subtract the depreciation rate from $1$ to find the factor by which the value decreases each year. $\newline$ Depreciation factor = $1 - r = 1 - 0.02 = 0.98$
Determine formula: Determine the formula to calculate the value of the car after a certain number of years $t$ . The formula for depreciation is: $\newline$ $V = P(1 - r)^t$ $\newline$ Where $V$ is the final value, $P$ is the initial value, $r$ is the depreciation rate, and $t$ is the number of years.
Plug in values: Plug in the values for $P$ , $r$ , and $t$ into the formula to find the equation that represents the value of the car after $2$ years. $\newline$ $V = 23,700(1 - 0.02)^2$ $\newline$ $V = 23,700(0.98)^2$
Check options: Check the provided options to see which one matches the correct equation. $\newline$ The correct equation is $V = 23,700(0.98)^2$ , which is not explicitly listed among the options. However, it is mathematically equivalent to the first option: $\newline$ $V = 23,700(1 - 0.02)^2$

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