What is the average rate of change of f(x)=2^x−1 over the interval 1≤x≤5 ?

Question

A) 7.5
B) 5
C) 8
D) -7.5

Answer 1

To find the average rate of change of a function over an interval, you can use the formula:
Average rate of change = (f(b) - f(a))/(b - a)

In this case, the interval is from 1 to 5, so a=1 and b=5.

f(1) = 2^1 - 1 = 2 - 1 = 1
f(5) = 2^5 - 1 = 32 - 1 = 31

So, the average rate of change = (31 - 1)/(5 - 1) = 30/4 = 7.5

Therefore, the average rate of change of f(x)=2^x−1 over the interval 1≤x≤5 is 7.5.

Therefore, the correct answer is (A) 7.5.