Question

For f(x) = 0.01(2)x, find the average rate of change from x = 3 to x = 8.

A- 0.08
B- 0.496
C- 2.48
D- 5

Answer 1

first plug in x = 3, what do you get?

\( f(3) = 0.01(2)^3\)

Answer 2

first do the exponents, what is 2^3 =

and then multiply by 0.01

Answer 3

idk

Answer 4

\( 2^3\) is the same thing as 2 * 2 * 2

what is 2 * 2 * 2 =

2 times 2 times 2 =

Answer 5

12

Answer 6

what is 2 times 2

Answer 7

i mean its 6. srry i was going by 4s lmaoo

Answer 8

are you sure?

what is 2 times 2

Answer 9

4

Answer 10

okay good, and what is 4 times 2

Answer 11

8

Answer 12

good now multiply that by 0.01

Answer 13

you can use a calculator

Answer 14

we then similarly have to do the same thing by plugging in x = 8

\(f(8) = 0.01(2)^8\)

Answer 15

and we need to then find the average rate of change or the slope

I'll throw in colors for you

\(\Large\text{Slope} = \dfrac{\color{green}{y_2} - \color{orange}{y_1}}{\color{cyan}{x_2}-\color{red}{x_1}}\)

where you have two points
\(\Large (\color{red}{x_1}, \color{orange}{y_1})\) and \(\Large (\color{cyan}{x_2}, \color{green}{y_2})\)

Answer 16

one of our points is (3, 0.08)

what value do you get when x = 8?