Question

4. Find and interpret theaverage rate of change forthe interval. Show your work.1

Answer 1

Answer:

Average rate of change = -2 celcius / hour

Interpretation: For every unit change in the time (x), there is a change of -2 celcius in the temperature

Explanations:

The average rate of change is to be found for the interval:

`1\text{ }\leq x\leq3`

From the interval, we can deduce that:

`x_1=1,x_2=3`

Know the corresponding value of y for each value of x shown above:

`\begin{gathered} \text{When x}_1=1,y_1=\text{ 6} \\ \text{When x}_2=3,y_2=\text{ 0} \end{gathered}`

The average rate of cgange is given by the formula:

`\begin{gathered} (\delta y)/(\delta x)=\text{ }(y_2-y_1)/(x_2-x_1) \\ (\delta y)/(\delta x)=\text{ }(0-6)/(3-1) \\ (\delta y)/(\delta x)=(-6)/(3) \\ (\delta y)/(\delta x)=-2 \end{gathered}`

The rate of change for the interval is -2 celcius/hour

This can be interpreted as for every unit change in the time (x), there is a change of -2 celcius in the temperature