Chapter ISG, Problem 3.3.11P

To determine

To calculate the rate of change

Answer to Problem 3.3.11P

Rate of change in the interval $x=-2$ to $x=2$ is,

-2

Rate of change in the interval $x=0$ to $x=4$ is,

0

Explanation of Solution

Given information:

The equation is,

  $y=-0.5x+4$

And the intervals are,

  $x=-2$ to $x=2$

And $x=0$ to $x=4$

Formula used:

Equation solving

Rate of change= $y2-y1$

Calculation:

For $x=-2$ to $x=2$

Substituting $x=-2$ in the equation,

  $y=\{-0.5\times (-2)\}+1$

So,

  $y=1+1$

On solving,

  $y=2$

Substituting $x=2$ in the equation,

  $y=(-0.5\times 2)+1$

So,

  $y=-1+1$

On solving,

  $y=0$

For the rate of change, substituting the value,

  $=0-2$

On solving,

  $=-2$

Hence, rate of change in the interval $x=-2$ to $x=2$ is,

-2

For $x=0$ to $x=4$

Substituting $x=0$ in the equation,

  $y=\{-0.5\times (0)\}+1$

On solving,

  $y=1$

Substituting $x=4$ in the equation,

  $y=\{-0.5\times 4\}+1$

So,

  $y=-2+1$

On solving,

  $y=-1$

For the rate of change, substituting the value,

  $=-1-1$

On solving,

  $=0$

Hence, rate of change in the interval $x=0$ to $x=6$ is,

0