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Consider the graph of f(x) = 5 ^ x + 1 1. Explain how to find the average rate of change between x = 0 and x = 4 . What is the average rate of change ?

Consider The Graph Of Fx 5 X 1 1 Explain How To Find The Average Rate Of Change Between X 0 And X 4 What Is The Average Rate Of Change class=

Sagot :

1. To determine the average rate of change of a function "f(x)" between the points "x = a" and "x = b" we use the following formula:

[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]

2. In this case, we have the following function:

[tex]f(x)=5^x+1[/tex]

And we have the points:

[tex]\begin{gathered} x=0 \\ x=4 \end{gathered}[/tex]

Now we determine the value of f(b) by replacing x = 4 in the function:

[tex]\begin{gathered} f(4)=5^4+1 \\ f(4)=626 \end{gathered}[/tex]

Now we determine f(0):

[tex]\begin{gathered} f(0)=5^0+1 \\ f(0)=1+1=2 \end{gathered}[/tex]

Replacing in the formula for the average rate of change we get:

[tex]A=\frac{626-2}{4-0}[/tex]

Solving the operations:

[tex]A=\frac{624}{4}=156[/tex]

Therefore, the average rate of change is 156.

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