Question
Leo's Mom purchased a car for $32,000. The value of her car decreases by 14% annually. You can use a function to describe the value of the car x yeas since Leo's mom bought it.
Match the below with the correct answer
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Is this Linear or Exponential ?
What formula would you need to solve this type of equation?
After 2 years what would the formula be for depreciation be on Leo's mom's Car?
What is the value of her car after 2 years?
Answers
GPT-4o mini
Let's break down your questions one at a time.
1. **Is this Linear or Exponential?**
- The value of Leo's mom's car decreases by 14% annually, which indicates that it is **Exponential** decay.
2. **What formula would you need to solve this type of equation?**
- The formula for exponential decay is:
\[
V(t) = V_0 (1 - r)^t
\]
where \( V(t) \) is the value of the car after \( t \) years, \( V_0 \) is the initial value of the car, \( r \) is the rate of decrease (in decimal form), and \( t \) is the number of years.
3. **After 2 years what would the formula be for depreciation be on Leo's mom's Car?**
- After 2 years, the formula for the value of the car would be:
\[
V(2) = 32000 \times (1 - 0.14)^2
\]
- Simplifying it:
\[
V(2) = 32000 \times (0.86)^2
\]
4. **What is the value of her car after 2 years?**
- Now calculating that value:
\[
V(2) = 32000 \times 0.7396 \quad (\text{since } 0.86^2 \approx 0.7396)
\]
\[
V(2) \approx 32000 \times 0.7396 \approx 23683.20
\]
So, the value of her car after 2 years is approximately **$23,683.20**.
Now, you can place these responses in the correct inputs according to your task.
1. **Is this Linear or Exponential?**
- The value of Leo's mom's car decreases by 14% annually, which indicates that it is **Exponential** decay.
2. **What formula would you need to solve this type of equation?**
- The formula for exponential decay is:
\[
V(t) = V_0 (1 - r)^t
\]
where \( V(t) \) is the value of the car after \( t \) years, \( V_0 \) is the initial value of the car, \( r \) is the rate of decrease (in decimal form), and \( t \) is the number of years.
3. **After 2 years what would the formula be for depreciation be on Leo's mom's Car?**
- After 2 years, the formula for the value of the car would be:
\[
V(2) = 32000 \times (1 - 0.14)^2
\]
- Simplifying it:
\[
V(2) = 32000 \times (0.86)^2
\]
4. **What is the value of her car after 2 years?**
- Now calculating that value:
\[
V(2) = 32000 \times 0.7396 \quad (\text{since } 0.86^2 \approx 0.7396)
\]
\[
V(2) \approx 32000 \times 0.7396 \approx 23683.20
\]
So, the value of her car after 2 years is approximately **$23,683.20**.
Now, you can place these responses in the correct inputs according to your task.