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The question from your image asks:

"It is estimated that the value of cars depreciates at a compound rate of 22% per year. Use this percentage to find the value of Pat's car after three years (original price €32,000)."

### Solution:

This is a compound depreciation problem, where the formula for compound depreciation is:

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

Where:
- \(V\) is the value of the car after time \(t\).
- \(P\) is the initial value (in this case €32,000).
- \(r\) is the depreciation rate per year (in this case 22%, or 0.22 as a decimal).
- \(t\) is the time in years (in this case 3 years).

Now, plugging in the values:

\[
V = 32,000 \times (1 - 0.22)^3
\]

Let me calculate this.The value of Pat's car after 3 years, depreciating at a rate of 22% per year, would be approximately €15,185.66.

Would you like more details on this process or have any other questions?

Here are five related questions for further practice:
1. What would the value of the car be after 5 years instead of 3 years?
2. If the depreciation rate was only 15% per year, what would be the value after 3 years?
3. How long would it take for the car's value to halve at a 22% depreciation rate?
4. What is the car's value after 1 year of depreciation?
5. How much value does the car lose after 3 years?

**Tip:** When working with percentages in problems, always convert them into decimals for calculations.

It is estimated that the value of cars depreciates at a compound rate of 22% per year. Use this percentage to find the value of Pat's car after three years (original price €32,000).

Learn how to calculate the depreciation of a car's value after 3 years, using a compound depreciation formula with a rate of 22% per year. The original value of the car is €32,000, and this step-by-step guide is suitable for students in Grades 10-12.

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