Question

Use the average rate of change to generate the function model for f(×)

Answer 1

The Solution:

Given:

We are required to use the rate of change to determine a function that models the given data.

The rate of change for each step in the data is:

`\begin{gathered} Rate\text{ of change}=(4-1)/(1-0)=(3)/(1)=3 \\ \\ \text{ Rate of change}=(7-4)/(2-1)=(3)/(1)=3 \\ \\ \text{Rate of change}=(12-7)/(3-2)=(5)/(1)=5 \end{gathered}`
`\begin{gathered} \text{Rate of change}=(15-12)/(4-3)=(3)/(1)=3 \\ \\ \text{Rate of change}=(19-15)/(5-4)=(4)/(1)=4 \\ \\ \text{Rate of change}=(22-19)/(6-5)=(3)/(1)=3 \end{gathered}`

So, the average rate of change is:

`Average\text{ rate of change}=(3+3+5+3+4+3)/(6)=(21)/(6)=3.5`

Thus, the model for f(x) is:

`f(x)=3.607x+0.6071`