PLEASE HELP 99 POINTSGiven the function h(x) = 3(5)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.Part A: Find the average rate of change of each section. (4 points)Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
Accepted Solution
A:
Presumably, [tex]h(x)=3(5)^x[/tex]. In that case,
(A) The average rate of change over the interval [tex]0\le x\le1[/tex] is
(B) [tex]\dfrac{300}{12}=25[/tex], i.e. the average rate of change over the second interval is 25 times higher. That's to be expected; [tex]3(5)^x[/tex] is an exponential function. As [tex]x[/tex] gets larger, the rate of change of [tex]h(x)[/tex] gets larger too.