Question

PLEASE HELP ME WITH THESE 3 QUESTIONS YOU GUYS! YOU WILL EARN ALOT OF POINT I PROMISE! 15+ PTS

1) Write a real world situation for the function f(x)=3(1.06^x)+2. Be sure to identify all key features of the function as what they represent in your situation.

2) In a paragraph, compare and contrast constant rate of change and average rate of change.

3) What is the average rate of change of the function g(x)=3(2^x)-6 over the interval 0<=x<=3? Show all work.

Answer 1

1) not sure of an example but it will be something with exponential growth.

2) Constant rate of change means the slope is the same between every point (always represented by a straight line). Average rate of change is the slope between the first and last point (not usually represented by a straight line).

3) g(x) = 3(2ˣ) - 6

g(0) = 3(2°) - 6 = 3(1) - 6 = 3 - 6 = -3 ⇒ coordinate (0, -3)

g(3) = 3(2³) - 6 = 3(8) - 6 = 24 - 6 = 18 ⇒ coordinate (3, 18)

average rate of change (slope) from x = 0 to x = 3:
`(y2 - y1)/(x2 - x1)`

`(18 - (-3))/(3 - 0)`

=
`(21)/(3)`

= 7