The equation V=25700(0.93)tV=25700(0.93)t represents the value (in dollars) of a car tt years after its purchase. Use this equation to complete the statements below.

The value of this car is Select an answer increasing decreasing  at a rate of  Select an answer percent per mile percent dollars dollars per year percent per year years

The purchase price of the car was  Select an answer dollars per year years percent dollars percent per year percent per mile  .

Let's analyze the equation and complete the statements. The given equation is:

\[
V = 25700(0.93)^t
\]

where $ V $ represents the value of the car in dollars, and $ t $ is the number of years after its purchase.

### 1. Is the value increasing or decreasing?

The term $ 0.93^t $ in the equation indicates a depreciation factor (since 0.93 is less than 1). This means the value of the car is decreasing over time.

### 2. At what rate is the car's value changing?

The car's value is decreasing by a factor of $ 0.93 $, which means it decreases by 7% each year (because $ 1 - 0.93 = 0.07 $).

### 3. What was the purchase price of the car?

At $ t = 0 $ (the time of purchase), the value of the car is:

\[
V(0) = 25700(0.93)^0 = 25700 \text{ dollars}
\]

### Completed Statements:

1. The value of this car is **decreasing** at a rate of **7 percent per year**.
2. The purchase price of the car was **25,700 dollars**.

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Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the value change if the depreciation rate were 5% instead of 7%?
2. After how many years will the car's value be half of its purchase price?
3. What would the car's value be after 10 years?
4. How would the equation change if the car’s value increased by 5% per year instead?
5. How would the purchase price change if the initial value were 30,000 dollars instead?

**Tip:** Depreciation in real-world contexts often follows exponential decay, just like in this problem. Understanding the formula's components is key to analyzing real-life investments!

The equation V=25700(0.93)^t represents the value (in dollars) of a car t years after its purchase. Use this equation to complete the statements below.

The value of this car is Select an answer increasing decreasing at a rate of Select an answer percent per mile percent dollars dollars per year percent per year years.

The purchase price of the car was Select an answer dollars per year years percent dollars percent per year percent per mile.

Understand how to calculate the depreciation of a car's value using the exponential decay formula V=25700(0.93)^t. Learn how the car's value decreases by 7% each year, with a purchase price of $25,700. Suitable for Grades 9-12 students.

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