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Let's break down and solve the given problem step by step:

### Part a) Construct a linear equation for the value $ V(t) $ of the backhoe as a function of its age $ t $ in years.

We are given:
- The initial value of the backhoe is $73,000.
- The backhoe depreciates linearly over 25 years.
- Its salvage value at the end of 25 years is $13,000.

The general equation of a line is in the form:
\[
V(t) = mt + b
\]
Where:
- $ m $ is the slope (rate of depreciation per year),
- $ t $ is the age in years,
- $ b $ is the initial value (when $ t = 0 $).

#### Step 1: Determine the slope $ m $.
The slope is the rate of depreciation, which is the change in value divided by the change in time:
\[
m = \frac{\text{final value} - \text{initial value}}{\text{time period}} = \frac{13000 - 73000}{25} = \frac{-60000}{25} = -2400
\]
So, the value of the backhoe decreases by $2,400 per year.

#### Step 2: Write the equation.
We know that at $ t = 0 $, $ V(0) = 73,000 $, so $ b = 73,000 $.

Thus, the equation for the value $ V(t) $ of the backhoe is:
\[
V(t) = -2400t + 73000
\]

### Part b) Use your model to find the value of the backhoe after 6 years.

We can substitute $ t = 6 $ into the equation \( V(t) = -2400t +

Depreciation is the decrease or loss in value of an item due to age, wear, or market conditions. One company buys a new backhoe for $73,000. The company depreciates the backhoe linearly over its useful life of 25 years. Its salvage value at the end of 25 years is $13,000. a) Construct a linear equation in the slope-intercept form that models the value, V(t), of the backhoe as a function of its age t in years. b) Use your model to find the value of the backhoe after 6 years.

Learn how to construct a linear equation to model the depreciation of a backhoe purchased for $73,000 with a salvage value of $13,000 after 25 years. Find the value after 6 years using the slope-intercept form. Suitable for Grades 9-11.

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