Sure, let's walk through the step-by-step process to find the current value of the car after 4 years using the depreciation formula.
1. Identify the given values:
- Original cost, [tex]\( A = \$ 24,000 \)[/tex]
- Rate of depreciation, [tex]\( r = 15\% \)[/tex] or [tex]\( 0.15 \)[/tex] (converted to a decimal)
- Time, [tex]\( t = 4 \)[/tex] years
2. Write down the depreciation formula:
[tex]\[
y = A(1 - r)^t
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
y = 24000 \times (1 - 0.15)^4
\][/tex]
4. Calculate the term inside the parentheses:
[tex]\[
1 - 0.15 = 0.85
\][/tex]
5. Raise the result to the power of 4:
[tex]\[
0.85^4 \approx 0.52200625
\][/tex]
6. Multiply this result by the original cost:
[tex]\[
y = 24000 \times 0.52200625 \approx 12528.15
\][/tex]
Therefore, the value of the car after 4 years is approximately [tex]$\$[/tex] 12,528.15$.
