Find the average rate of change for the function f(x)=3^x+25 Using the intervals of x=2 to x=6
f(2) = 3^2 + 25 = 34
f(6) = 3^6 + 25 = 729+25 = 754
avg rate of change = change in y / change in x
= (754-34)/(6-2) = 720/4 = 180
I really need your help!
Thank you so much! I did not have any idea how to even begin!
To find the average rate of change for the function f(x) = 3^x + 25 over the interval x = 2 to x = 6, you can use the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where f(a) is the value of the function at the lower limit of the interval (a) and f(b) is the value of the function at the upper limit of the interval (b).
In this case, the lower limit of the interval is x = 2 and the upper limit is x = 6. We need to find the values of f(2) and f(6) to calculate the average rate of change.
To find f(2), plug in x = 2 into the function:
f(2) = 3^2 + 25 = 9 + 25 = 34
To find f(6), plug in x = 6 into the function:
f(6) = 3^6 + 25 = 729 + 25 = 754
Now we have the required values to calculate the average rate of change:
Average rate of change = (f(6) - f(2)) / (6 - 2)
= (754 - 34) / (6 - 2)
= 720 / 4
= 180
Therefore, the average rate of change for the function f(x) = 3^x + 25 over the interval x = 2 to x = 6 is 180.