Question

what is the average rate of change for this exponential function for the interval from x = 0 to x = 2?
text description for graph
a. -4
b. 4
c. 1.5
d. -1.5

Explanation:

Step1: Find the function values at endpoints

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here \(a = 0\), \(b=2\). From the graph, when \(x = 0\), \(y=f(0)=1\); when \(x = 2\), \(y=f(2)=4\).

Step2: Calculate the average rate of change

Substitute into the formula: \(\frac{f(2)-f(0)}{2-0}=\frac{4 - 1}{2}=\frac{3}{2}=1.5\)

Answer:

C. 1.5