Question

For f(x) = 0.01(2)x, find the average rate of change from x = 2 to x = 10. 1.275 8 10.2 10.24

Answer 1

Answer:

The average rate of change of f(x) from x=2 to x=10 is:

                            1.275

Step-by-step explanation:

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

$Rate\ of\ change=\dfrac{f(b)-f(a)}{b-a}$

The function f(x) is given by:

$f(x)=0.01\cdot 2^x$

We need to find the average rate of change of f(x) from x=2 to x=10

Hence, the average rate of change is calculated by:

$Rate\ of\ change=\dfrac{f(10)-f(2)}{10-2}\\\\i.e.\\\\Rate\ of\ change=\dfrac{0.01\cdot 2^{10}-0.01\cdot 2^2}{8}\\\\Rate\ of\ change=\dfrac{0.01\times 2^2(2^8-1)}{8}\\\\i.e.\\\\Rate\ of\ change=\dfrac{0.01\times 255}{2}\\\\Rate\ of\ change=1.275$

         Hence, the answer is:  1.275

Answer 2

The average rate of change is ...

... (change in f(x))/(change in x)

... = (f(10) - f(2))/(10 - 2)

... = (10.24 - 0.04)/8 = 10.2/8 = 1.275