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 +