Question

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

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 :-

$k=\dfrac{f(b)-f(a)}{b-a}$

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

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

$k=\dfrac{f(10)-f(2)}{10-2}$

$=\dfrac{0.01(2)^{10}-0.01(2)^{2}}{8}\\\\=\dfrac{0.01(1024)-0.01(4)}{2}\\\\=\dfrac{10.24-0.04}{2}\\\\=\dfrac{10.20}{8}=1.275$

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

Answer 2

Answer:

1.275

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 = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{10.24-0.04}{10-2} =\frac{10.2}{8} =1.275$

Hope this helps :)