Question

Find the average rate of change from x = 3 to x = 15 for the function f(x) = 0.01(2)x and select the correct answer below.

A0.08
B12
C27.3
D327.68

Answer 1

Answer: C. 27.3

Explanation:

The average rate of function f(x) from x = a to x = b is given by :-

`k=(f(b)-f(a))/(b-a)`

The given function :
`f(x) = 0.01(2)^x`

Now, the average rate of function f(x) from x = 3 to x = 15 is given by :-

`k=(f(15)-f(3))/(15-3)\\\\\Rightarrow\ k=(0.01(2)^(15)-0.01(2)^3)/(12)\\\\\Rightarrow\ k=27.3`

Hence, the average rate of change from x = 3 to x = 15 for the given function = 27.3 .

Answer 2

x=3:

0.01*2^3 = 0.08

x=15:

0.01*2^15 = 327.68

327.68 - 0.08 = 327.60

15-3 = 12

327.6/12 = 27.3

Answer is C