The average rate of change for the function f(x)= 3^x + 25 using the intervals of x=2 to x=6 is 6.75
The function is given as:
f(x) = 3^x + 25
The interval is given as:
x = 2 to 6
Start by calculating f(2) and f(6)
f(2) = 3^2 + 25 = 34
f(6) = 6^2 + 25 = 61
The average rate of change is then calculated as:
[tex]m = \frac{f(6) - f(2)}{6 -2}[/tex]
This gives
[tex]m = \frac{61 - 34}{6 -2}[/tex]
[tex]m = \frac{27}{4}[/tex]
m = 6.75
Hence, the average rate of change is 6.75
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