Question
A new car is purchased for 28,900 dollars. The value of the car depreciates at a rate of 5% per year. Which equation represents the value of the car after 3 years?
Answers
GPT-4o mini
To represent the value of the car after 3 years, we can use the formula for exponential decay due to depreciation. The formula for the value \( V \) of the car after \( t \) years is given by:
\[
V = P(1 - r)^t
\]
where:
- \( P \) is the initial value of the car,
- \( r \) is the depreciation rate (expressed as a decimal),
- \( t \) is the number of years.
In this case:
- \( P = 28,900 \) (the initial value of the car),
- \( r = 0.05 \) (5% depreciation rate),
- \( t = 3 \) (number of years).
Substituting these values into the formula:
\[
V = 28,900 \times (1 - 0.05)^3
\]
This simplifies to:
\[
V = 28,900 \times (0.95)^3
\]
Thus, the equation that represents the value of the car after 3 years is:
\[
V = 28,900 \times (0.95)^3
\]
\[
V = P(1 - r)^t
\]
where:
- \( P \) is the initial value of the car,
- \( r \) is the depreciation rate (expressed as a decimal),
- \( t \) is the number of years.
In this case:
- \( P = 28,900 \) (the initial value of the car),
- \( r = 0.05 \) (5% depreciation rate),
- \( t = 3 \) (number of years).
Substituting these values into the formula:
\[
V = 28,900 \times (1 - 0.05)^3
\]
This simplifies to:
\[
V = 28,900 \times (0.95)^3
\]
Thus, the equation that represents the value of the car after 3 years is:
\[
V = 28,900 \times (0.95)^3
\]