Answer:
The average rate of change in section 2 is 25 times larger than the average rate of change in section 1.
Step-by-step explanation:
Recall that the average rate of change of a function [tex]f(x)[/tex] in an interval [a,b] (section of the number line) is defined as:
Rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Therefore:
1) First interval: evaluating the rate of change from x=0, to x=1 (interval [0, 1]) it becomes
Rate of change = [tex]\frac{f(b)-f(a)}{b-a}=\frac{f(1)-f(0)}{1-0}=\frac{5^1-5^0}{1}=5-1=4[/tex]
2) Second interval: we now evaluate the rate of change from x=2 to x=3 (interval [2, 3]), so it becomes
[tex]\frac{f(b)-f(a)}{b-a}=\frac{f(3)-f(2)}{3-2}=\frac{5^3-5^2}{1}=125-25=100[/tex]
Therefore, the rate of change in the second interval is much larger than the rate of change in the first one. The second rate of change is in fact 100/4 = 25 times larger than the first rate of change. this is due to the fact that the function is an exponential function and not a linear function (where the rate of change is constant)
