Question

What is the average rate of change for f(x)=2^x+10 over the interval
`2 \leqslant x \leqslant 4`A. 4B. 6C. 8 D. 12

Answer 1

Step 1 :

In this question, we are meant to calculate the average rate of the change over the

interval

`\begin{gathered} 2\text{ }\leq\text{ x }\leq\text{ 4} \\ \text{where f ( x ) = 2}^x\text{ + 10} \end{gathered}`

Step 2 :

For the average rate of change, we need to do the following calculations:

`\frac{f(\text{ 4 ) - f( 2)}}{4-\text{ 2 }}`

putting x = 4 in

`\begin{gathered} f(4)=2^4\text{ + 10 } \\ =\text{ 16 + 10 } \\ =\text{ 26} \end{gathered}`

putting x = 2 in

`\begin{gathered} f(2)=2^{2\text{ }}+\text{ 10} \\ =\text{ 4 + 10} \\ =14 \end{gathered}`
`\frac{f\text{ ( 4 ) - f( 2 )}}{4\text{ - 2 }}\text{ = }\frac{26\text{ - 14}}{4\text{ - 2}}\text{ = }(12)/(2)\text{ = 6}`

CONCLUSION: The average rate of change = 6.