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A new car is purchased for 29,900 dollars. The value of the car depreciates at a rate of
2.7% per year. Which equation represents the value of the car after 4 years?

V=29,900(1-0.027)(1-0.027)(1-0.027)

V=29,900(0.973)^(4)

V=29,900(1.027)^(4)

V=29,900(1+0.027)^(4)

A new car is purchased for $29$ , $900$ dollars. The value of the car depreciates at a rate of $2.7 \%$ per year. Which equation represents the value of the car after $4$ years? $\newline$ $V=29,900(1-0.027)(1-0.027)(1-0.027)$ $\newline$ $V=29,900(0.973)^{4}$ $\newline$ $V=29,900(1.027)^{4}$ $\newline$ $V=29,900(1+0.027)^{4}$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. A new car is purchased for

29

,

900

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

2.7 \%

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

4

years?

\newline

V=29,900(1-0.027)(1-0.027)(1-0.027)

\newline

V=29,900(0.973)^{4}

\newline

V=29,900(1.027)^{4}

\newline

V=29,900(1+0.027)^{4}

Identify values: Identify the initial value of the car and the annual depreciation rate. $\newline$ Initial value $P$ = $\$29,900$ $\newline$ Annual depreciation rate $r$ = $2.7\%$ or $0.027$ in decimal form.
Understand formula: Understand the formula for depreciation. The value of the car after a certain number of years can be calculated using the formula for exponential decay: $V = P(1 - r)^t$ , where $V$ is the final value, $P$ is the initial value, $r$ is the depreciation rate, and $t$ is the time in years.
Substitute values: Substitute the given values into the formula. We need to find the value of the car after $4$ years $t = 4$ . $V = 29,900(1 - 0.027)^4$
Calculate inside parentheses: Calculate the value inside the parentheses. $1 - 0.027 = 0.973$
Raise to power: Raise $0.973$ to the power of $4$ to represent the depreciation over $4$ years. $\newline$ $(0.973)^4$
Write final equation: Write the final equation with the calculated values. $\newline$ $V = 29,900(0.973)^4$ $\newline$ This is the equation that represents the value of the car after $4$ years.

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