Question

part 1 of 4 (a) how much will a computer be worth 1 yr after purchase? one year after the purchase, the computer will be worth $1200 part 2 of 4 (b) after how many years will the computer be worth only $400? after 3 yr, the computer will be worth only $400. part 3 of 4 (c) determine the y - intercept and interpret its meaning in the context of this problem. the y - intercept is and it represents the select value.

Explanation:

Step1: Assume linear - depreciation model

Let the value of the computer $V$ be a linear function of time $t$ (in years), $V(t)=mt + b$. We know two points: $(1,1200)$ and assume the initial value at $t = 0$ is $V(0)=b$ and another point $(t_1,400)$. First, we need to find the slope $m$.

Step2: Find the slope $m$

If we assume the computer depreciates linearly, and we know when $t = 1$, $V=1200$ and when $t = 3$, $V = 400$. The slope $m=\frac{400 - 1200}{3 - 1}=\frac{- 800}{2}=-400$.

Step3: Find the $y$ - intercept

Using the point - slope form $V - V_1=m(t - t_1)$ with the point $(1,1200)$ and $m=-400$. Substitute into $V=mt + b$, when $t = 1$ and $V = 1200$, we have $1200=-400\times1 + b$. Solving for $b$ gives $b=1200 + 400=1600$.

Answer:

The $y$-intercept is $1600$ and it represents the initial value.