Question

Question 9 of 25

This table shows values that represent an exponential function.
1
2
3
4
5
y
7
9
13
21
37
What is the average rate of change for this function for the interval from x = 1
to x = 3?

Answer 1

Explanation:

To find the average rate of change for an exponential function over an interval, we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where “a” and “b” are the endpoints of the interval, and “f” is the exponential function.

In this case, the interval is from x = 1 to x = 3, so a = 1 and b = 3. We are given the values of the function for these inputs:

f(1) = 7

f(2) = 9

f(3) = 13

Substituting these values into the formula, we get:

average rate of change = (f(3) - f(1)) / (3 - 1)

average rate of change = (13 - 7) / 2

average rate of change = 3

Therefore, the average rate of change for this function over the interval from x = 1 to x = 3 is 3.