A new car is purchased for 17600 dollars. The value of the car depreciates at 11.75% per year. What will the value of the car be, to the nearest cent, after 11 years?

To find the value of the car after 11 years, we use the formula for exponential depreciation:

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

where:
- $ V(t) $ is the value of the car after $ t $ years,
- $ P $ is the initial value of the car,
- $ r $ is the depreciation rate per year (expressed as a decimal),
- $ t $ is the number of years.

Given:
- $ P = 17600 $ dollars,
- $ r = 11.75\% = 0.1175 $,
- $ t = 11 $ years.

Now we can plug the values into the formula:

\[
V(11) = 17600 \times (1 - 0.1175)^{11}
\]

Let's calculate that.The value of the car after 11 years will be approximately **$4450.15**.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. What would the car's value be after 15 years at the same depreciation rate?
2. How long would it take for the car to lose half of its value?
3. What if the depreciation rate changed to 9% per year? How would that affect the value after 11 years?
4. What is the percentage of the car's value lost after 5 years?
5. Can we model this depreciation using continuous compounding instead?

**Tip:** Depreciation is often modeled exponentially because it reflects the continuous percentage loss of value over time.

Learn how to calculate the depreciation of a car purchased for $17,600 with a yearly depreciation rate of 11.75%. Find out the car's value after 11 years using the exponential depreciation formula. Ideal for high school students in Grades 9-12.

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