Question

The value of a 2024 Toyota Prius was $44,205 when it went on the market. It depreciates at a rate of 10.5% per year
decay or growth
r-value?
function?

Answer 1

To analyze the value of a 2024 Toyota Prius that depreciates at a rate of 10.5% per year, we can describe this situation using an exponential decay model.

### 1. **Decay vs. Growth:**
- This situation represents **decay** because the value of the car decreases over time.

### 2. **r-value:**
- The decay rate (r-value) is the percentage by which the value decreases annually. Here, r = 10.5%, which can be expressed as a decimal:
\[
r = 0.105
\]

### 3. **Function:**
- The value of the car after \( t \) years can be modeled by the exponential decay function:
\[
V(t) = V_0 \cdot (1 - r)^t
\]
where:
- \( V(t) \) is the value of the car after \( t \) years,
- \( V_0 \) is the initial value of the car (which is $44,205),
- \( r \) is the rate of depreciation (0.105),
- \( t \) is the number of years since the car was purchased.

Plugging in the values into the function, we get:
\[
V(t) = 44205 \cdot (1 - 0.105)^t
\]
\[
V(t) = 44205 \cdot (0.895)^t
\]

### Summary:
- This situation involves **decay**, with a decay rate of **10.5%**.
- The value of the car can be modeled by the function:
\[
V(t) = 44205 \cdot (0.895)^t
\]