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The question on the screen asks about the depreciation of a car purchased for $20,000. Here's the breakdown:

### Part (a):
You are asked to write an equation representing the car’s value, $ V(t) $, after $ t $ years, given that the car depreciates by 12% each year. 

The general formula for exponential depreciation is:

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

Where:
- $ a $ is the initial value ($20,000),
- $ r $ is the depreciation rate (12% = 0.12),
- $ t $ is the number of years.

Substituting the given values into the formula:

\[
V(t) = 20000 \cdot (1 - 0.12)^t = 20000 \cdot (0.88)^t
\]

### Part (b):
For $ t = 10 $ years, we need to calculate the approximate value of the car.

\[
V(10) = 20000 \cdot (0.88)^{10}
\]

Let me calculate that for you.The approximate value of the car after 10 years is **$5,570.02**.

Do you want any further details or clarifications on this problem?

Here are some related questions:
1. How does the depreciation formula change if the depreciation rate increases?
2. How would you calculate the car's value after 5 years?
3. What is the percentage decrease in the car's value after 10 years?
4. How would you set up the formula if the depreciation rate was 10% instead of 12%?
5. Can this model be used for non-linear depreciation rates? Why or why not?

**Tip:** The base in an exponential depreciation model reflects the remaining value after each period, and it is always less than 1 for depreciation.

Tom bought a car for $20,000 and the car depreciates 12% each year. Write an equation in the form V(t) = a(b)^t that would represent the value of the car 't' years after its purchase. What is the approximate value of the car, 10 years after its purchase?

Learn how to calculate the value of a car that depreciates at a rate of 12% per year using the exponential decay formula. The problem starts with a car valued at $20,000 and asks for the car's value after 10 years. Suitable for high school students (Grades 9-12).

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