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The question in the image states:

**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.**

Let's break it down:

1. **Initial Value:** The car starts at $20,000, so $ a = 20,000 $.
2. **Depreciation:** The car loses 12% of its value each year, which means it retains 88% of its value each year (since $ 100\% - 12\% = 88\%$). Therefore, $ b = 0.88 $.

So the equation becomes:

\[
V(t) = 20000(0.88^t)
\]

**Next, it asks: What is the approximate value of the car, 10 years after its purchase?**

To find that, substitute $ t = 10 $ into the equation:

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

Let's calculate the value of the car after 10 years.The approximate value of the car 10 years after its purchase is **$5,570.02**.

Do you want further clarification or details on the steps? Here are some related questions to expand your understanding:

1. How would the equation change if the depreciation rate were different?
2. How can you calculate the car's value after 5 years instead of 10?
3. What would happen if the car's depreciation rate was compounded monthly instead of annually?
4. Can the depreciation rate be modeled using a different type of function, such as a logarithmic function?
5. How would the model change if the depreciation rate varied each year?

**Tip:** Depreciation problems can often be modeled using exponential decay equations, which are useful for any context where a value decreases by a fixed percentage over time.

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 a car t years after its purchase. What is the approximate value of the car, 10 years after its purchase? Round your answer to the nearest cent.

Learn how to calculate the depreciation of a car bought for $20,000 with a 12% yearly depreciation. This guide includes the exponential decay formula V(t) = a(b^t) and finds the approximate car value after 10 years. Suitable for students in Grades 9-12.

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