A new car is purchased for 15500 dollars. The value of the car depreciates at 7.5% per year. What will the value of the car be, to the nearest cent, after 6 years?

To find the value of the car after 6 years, we can use the formula for exponential depreciation:

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

Where:
- $ V(t) $ is the value of the car after $ t $ years,
- $ P $ is the initial value of the car (in this case, 15,500 dollars),
- $ r $ is the annual depreciation rate (7.5% = 0.075),
- $ t $ is the number of years (6 years).

### Step-by-step calculation:

1. Initial value $ P = 15,500 $
2. Depreciation rate $ r = 0.075 $
3. Time $ t = 6 $ years

Now, plug these into the formula:

\[
V(6) = 15,500(1 - 0.075)^6
\]
\[
V(6) = 15,500(0.925)^6
\]
\[
V(6) \approx 15,500(0.6506)
\]
\[
V(6) \approx 10,084.30
\]

So, the value of the car after 6 years will be approximately **$10,084.30**.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What would the value of the car be after 10 years at the same depreciation rate?
2. How long will it take for the car's value to drop below $5,000?
3. If the depreciation rate were 5% instead, what would be the value after 6 years?
4. How would the formula change if the car appreciated in value instead of depreciating?
5. What would the car's value be if it were purchased for $20,000 with the same depreciation rate?

**Tip:** When dealing with percentage changes over time, exponential decay or growth is often the best model to use.

Discover how to calculate the value of a car purchased for $15,500 that depreciates at a 7.5% annual rate. Using the exponential decay formula, find the value after 6 years to the nearest cent. Perfect for high school students learning about depreciation and exponential decay.

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