Question

For f(x) = 0.01(2)x, find the average rate of change from x = 2 to x = 10.

Select one:
a. 1.275
b. 8
c. 10.2
d. 10.24

Answer 1

Answer: a. 1.275

Step-by-step explanation:

Let f(x) be any function.

Then the average rate of change 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`

Then, the average rate of change from x = 2 to x = 10 will be :-

`k=(f(10)-f(2))/(10-2)`

`=(0.01(2)^(10)-0.01(2)^(2))/(8)\\\\=(0.01(1024)-0.01(4))/(2)\\\\=(10.24-0.04)/(2)\\\\=(10.20)/(8)=1.275`

Hence, the average rate of change from x = 2 to x = 10 is 1.275.

Answer 2

1.275

Step-by-step explanation:

The given equation is:

f(x) = 0.01(2)ˣ

We want to find the rate of change from 2 to 10 which means that we need to find the slope from 2 to 10.

We start by getting the y-values for each of the given x-values:

at x = 2 ..........> y = 0.01(2)² = 0.04 ...........> point is (2, 0.04)

at x = 10 .........> y = 0.01(2)¹⁰ = 10.24 .........> point is (10, 10.24)

Now, we get the slope as follows:

slope =
`(y_(2)-y_(1))/(x_(2)-x_(1)) = (10.24-0.04)/(10-2) =(10.2)/(8) =1.275`

Hope this helps :)