Question

A car's value depreciates at a rate of 3.4% per year. The car was worth $30,000 when it was new.



Which equation could be used to determine when the car will be worth $18,500, where x is time in years?

Answer options with 4 options
A.
18500 equals 30000 left-parenthesis 0.034 right-parenthesis Superscript x Baseline

B.
18500 equals 30000 left-parenthesis 0.966 right-parenthesis Superscript x Baseline

C.
30000 equals 18500 left-parenthesis 0.034 right-parenthesis Superscript x Baseline

D.
30000 equals 18500 left-parenthesis 0.966 right-parenthesis Superscript x Baseline

Answer 1

To determine the equation that describes the depreciation of the car, we can use the formula for exponential decay:

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

Where:
- \( V \) is the value of the car after \( x \) years,
- \( P \) is the initial value of the car,
- \( r \) is the depreciation rate (as a decimal),
- \( x \) is the time in years.

In this case:
- The initial value \( P \) is $30,000.
- The depreciation rate \( r \) is 3.4%, which is 0.034 as a decimal.
- We want to find out when the value \( V \) is $18,500.

Substituting those values into the equation gives us:

\[
18500 = 30000(1 - 0.034)^x
\]

This simplifies to:

\[
18500 = 30000(0.966)^x
\]

Thus, the correct equation is:

**B. 18500 equals 30000(0.966)^x**