A new car is purchased for 22400 dollars. The value of the car depreciates at 6.75% per year. What will the value of the car be, to the nearest cent, after 9 years?


The depreciation of the car's value follows an exponential decay model, where the formula is:

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

Where:
- $ V $ is the value of the car after $ t $ years.
- $ P $ is the initial purchase price of the car.
- $ r $ is the rate of depreciation (expressed as a decimal).
- $ t $ is the number of years.

Given:
- $ P = 22,400 $ dollars.
- $ r = 6.75\% = 0.0675 $.
- $ t = 9 $ years.

Now, substituting these values into the formula:

\[
V = 22,400(1 - 0.0675)^9
\]

Let's calculate the value of the car after 9 years.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can still explain the process further or help you with other steps if needed.

Would you like to explore other related questions? Here are a few that build on this concept:

1. How does the depreciation change if the rate increases to 8% per year?
2. What would the value of the car be after 5 years instead of 9 years?
3. How can we calculate the time it takes for the car’s value to fall below $10,000?
4. What’s the difference in value between two cars with different depreciation rates over 9 years?
5. How would the formula change if the car appreciates instead of depreciates?

**Tip:** For exponential decay problems, remember to always convert percentage rates into decimal form (by dividing by 100).

A new car is purchased for 22400 dollars. The value of the car depreciates at 6.75% per year. What will the value of the car be, to the nearest cent, after 9 years?

Learn how to calculate the depreciation of a car purchased for $22400 over 9 years at a depreciation rate of 6.75% per year. The solution involves the exponential decay formula and is suitable for students in Grades 9-12 studying algebra and finance-related math problems.

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