The average rate of change, of the function, between the intervals, x = 2 to x = 6 is: 180.
What is the Average Rate of Change of a Function?
Average rate of change = [tex]\frac{f(b) - f(a)}{b - a}[/tex].
Given the function, [tex]f(x)= 3^x + 25[/tex],
The average rate of change using the intervals of, x = 2 to x = 6 would be solved as shown below:
a = 2
b = 6
f(a) = [tex]f(2)= 3^2 + 25[/tex] = 34
f(b) = [tex]f(6)= 3^6 + 25[/tex] = 754
Average rate of change = [tex]\frac{754 - 34}{6 - 2} = \frac{720}{4}[/tex]
Average rate of change = 180
Therefore, the average rate of change, of the function, between the intervals, x = 2 to x = 6 is: 180.
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