Question

the value of a computer t years after purchase is given by v(t)=1000 - 200t, where v(t) is in dollars. find the average rate of change of the value of the computer on the interval 0,3.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = v(t)$ on the interval $[a,b]$ is $\frac{v(b)-v(a)}{b - a}$. Here, $a = 0$, $b = 3$, and $v(t)=1000 - 200t$.

Step2: Calculate $v(3)$ and $v(0)$

When $t = 3$, $v(3)=1000-200\times3=1000 - 600 = 400$. When $t = 0$, $v(0)=1000-200\times0 = 1000$.

Step3: Compute the average rate of change

$\frac{v(3)-v(0)}{3 - 0}=\frac{400 - 1000}{3}=\frac{- 600}{3}=-200$.

Answer:

$-200$