contestada

PLEASE HELP 99 POINTS

Given 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)

Respuesta :

LammettHash
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

[tex]\dfrac{h(1)-h(0)}{1-0}=\dfrac{15-3}1=12[/tex]

and over [tex]2\le x\le3[/tex], it's

[tex]\dfrac{h(3)-h(2)}{3-2}=\dfrac{375-75}1=300[/tex]

(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.

Presumably, . In that case,

(A)

The average rate of change over the interval  is

and over , it's

(B)

, i.e. the average rate of change over the second interval is 25 times higher. That's to be expected;  is an exponential function. As  gets larger, the rate of change of  gets larger too.

Otras preguntas