annalisa wants to buy a harley davidson motorcycle. The model she wants to purchase costs $26,100 and straight line depreciates for 18 years. 1-what is the rate of depreciation for the motorcycle? 2- what is the straight like depreciation equation? 3- if she wants to sell the motorcycle after 5 years, how much should it be worth? 4- when will the motorcycle be worth 11.600?

We are given that Annalisa wants to purchase a Harley Davidson motorcycle that costs $26,100 and straight-line depreciates over 18 years. We will calculate the rate of depreciation, the depreciation equation, the value after 5 years, and the time when the motorcycle's value will be $11,600.

### 1. What is the rate of depreciation for the motorcycle?

The rate of depreciation in straight-line depreciation is calculated by dividing the total initial cost of the motorcycle by the number of years over which it depreciates:

\[
\text{Rate of Depreciation} = \frac{\text{Initial Value}}{\text{Years of Depreciation}} = \frac{26,100}{18}
\]

\[
\text{Rate of Depreciation} = 1,450 \, \text{per year}
\]

### 2. What is the straight-line depreciation equation?

The straight-line depreciation equation is of the form:

\[
V(t) = V_0 - D \cdot t
\]

Where:
- $V(t)$ is the value of the motorcycle after $t$ years.
- $V_0$ is the initial value of the motorcycle ($26,100).
- $D$ is the rate of depreciation per year ($1,450).
- $t$ is the time in years.

Thus, the equation becomes:

\[
V(t) = 26,100 - 1,450 \cdot t
\]

### 3. If she wants to sell the motorcycle after 5 years, how much should it be worth?

We substitute $t = 5$ into the depreciation equation to find the value after 5 years:

\[
V(5) = 26,100 - 1,450 \cdot 5
\]
\[
V(5) = 26,100 - 7,250
\]
\[
V(5) = 18,850
\]

After 5 years, the motorcycle should be worth **$18,850**.

### 4. When will the motorcycle be worth $11,600?

We now solve for $t$ when $V(t) = 11,600$:

\[
11,600 = 26,100 - 1,450 \cdot t
\]
\[
1,450 \cdot t = 26,100 - 11,600
\]
\[
1,450 \cdot t = 14,500
\]
\[
t = \frac{14,500}{1,450} = 10
\]

The motorcycle will be worth **$11,600** after **10 years**.

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Do you want further details or have any questions? 

Here are 5 related questions to extend the topic:
1. What would be the value of the motorcycle after 12 years?
2. How much value does the motorcycle lose after 8 years?
3. What is the total depreciation after 18 years?
4. How much value is retained after 15 years?
5. If the depreciation rate changed to 10 years, how would the equation change?

**Tip:** Straight-line depreciation is useful for assets like vehicles where depreciation happens evenly over time.

Annalisa wants to buy a Harley Davidson motorcycle. The model she wants to purchase costs $26,100 and straight-line depreciates for 18 years. 1. What is the rate of depreciation for the motorcycle? 2. What is the straight-line depreciation equation? 3. If she wants to sell the motorcycle after 5 years, how much should it be worth? 4. When will the motorcycle be worth $11,600?

Learn how to calculate the straight-line depreciation of a Harley Davidson motorcycle that costs $26,100, depreciates over 18 years, and find out its worth after 5 years or when it reaches $11,600. This solution involves algebra and linear depreciation formulas, suitable for students in Grades 9-12.

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