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.

A. 0.08
B. 12
C. 27.3
D. 327.68

Answer 1

Excuse me but his answer is incorrect. To find the proper rate of change you might have to solve it like you would for slope.
First you would find the points for x = 3 and x = 15 would be (3, 0.08) and (15, 327.68). Then using the slope formula you can find 327.60/ 12. That gives 27.3. So in that case the correct answer is C.

Answer 2

Option C is correct

27.3

Explanation:

Average rate of change A(x) of f(x) over interval [a, b] is given by:

`A(x) = (f(b)-f(a))/(b-a)` .....[1]

As per the statement:

Given the function:

`f(x) = 0.001 \cdot 2^x`

At x = 3

then;

`f(3) = 0.001 \cdot 2^3 = 0.01 \cdot 8 = 0.08`

At x = 15

then;

`f(3) = 0.001 \cdot 2^15 = 0.01 \cdot 32768= 327.68`

Substitute these given values in [1] we have;l

`A(x) = (f(15)-f(3))/(15-3) = (3267.8-0.08)/(12) =(327.6)/(12) = 27.3`

Therefore, the average rate of change from x = 3 to x = 15 is, 27.3