B 11. Solve, assuming a linear equation fits the situation. The value of a computer is \( \$ 3500 \). After 2 years, the value of this computer is \( \$ 2200 \). Find the value of the computer after 5 years.

To determine the value of the computer after 5 years using a linear equation, follow these steps: ### **1. Define Variables** - Let \( t \) represent the number of years since the purchase. - Let \( V(t) \) represent the value of the computer after \( t \) years. ### **2. Set Up the Linear Equation** Assume the value of the computer decreases linearly over time. The general form of a linear equation is: \[ V(t) = mt + b \] where: - \( m \) is the slope (rate of change per year), - \( b \) is the y-intercept (initial value when \( t = 0 \)). ### **3. Determine the Y-Intercept (\( b \))** At \( t = 0 \) (the time of purchase), the value of the computer is \$3500: \[ V(0) = m(0) + b = 3500 \] \[ b = 3500 \] ### **4. Use the Second Data Point to Find the Slope (\( m \))** After 2 years, the value drops to \$2200: \[ V(2) = m(2) + 3500 = 2200 \] \[ 2m + 3500 = 2200 \] \[ 2m = 2200 - 3500 \] \[ 2m = -1300 \] \[ m = \frac{-1300}{2} \] \[ m = -650 \] ### **5. Write the Complete Linear Equation** Now, substitute \( m \) and \( b \) back into the equation: \[ V(t) = -650t + 3500 \] ### **6. Calculate the Value After 5 Years** Plug \( t = 5 \) into the equation: \[ V(5) = -650(5) + 3500 \] \[ V(5) = -3250 + 3500 \] \[ V(5) = 250 \] ### **Conclusion** After **5 years**, the value of the computer will be **\$250**.