WORD PROBLEM

Question

Leo's Mom purchased a car for $32,000. The value of her car decreases by 14% annually. You can use a function to describe the value of the car x yeas since Leo's mom bought it.

Match the below with the correct answer

(3 points)

Answer 1

To represent the value of the car as a function of time, we can use the formula for exponential decay. The value of an asset after a certain period can be calculated using the formula:

\[ V(x) = V_0(1 - r)^x \]

where:

• \( V(x) \) is the value of the car after \( x \) years,
• \( V_0 \) is the initial value of the car (in this case, $32,000),
• \( r \) is the rate of depreciation (14% annually, or 0.14),
• \( x \) is the number of years since the car was purchased.

So plugging in the values:

\[ V(x) = 32000(1 - 0.14)^x \] \[ V(x) = 32000(0.86)^x \]

Now, based on this function definition, the options you presented can be matched as follows:

1. Initial Value of the car: $32,000
2. Rate of depreciation: 14% (or 0.14)
3. Formula function: \( V(x) = 32000(0.86)^x \)

If there are specific options you need matched, please provide those!