Question

Please help:The table of values represents an exponential function f(x).What is the average rate of change over the interval −1 ≤ x ≤ 3?Enter your answer, as a decimal rounded to the nearest hundredth, in the box. ___xf(x)−1130113293274815243

Answer 1

The average rate of change of a function in the interval [a,b] is given by:

`m=(f(b)-f(a))/(b-a)`

In this case we know that the interval is [-1,3] which means that a=-1 and b=3. This also means that we need to find f(-3) and f(-1); from the table we have:

`\begin{gathered} f(-1)=(1)/(3) \\ f(3)=27 \end{gathered}`

Once we know all the values, we need we plug them in the expression for the average rate of change:

`\begin{gathered} m=(f(3)-f(-1))/(3-(-1)) \\ =(27-(1)/(3))/(3+1) \\ =((81-1)/(3))/(4) \\ =((80)/(3))/(4) \\ =(80)/(12) \\ =(20)/(3) \\ =6.67 \end{gathered}`

Therefore, the average rate of change of the function in that interval is 6.67.