Question

For f(x) = 0.01(2)x, find the average rate of change from x = 12 to x = 15.

3
40.96
95.57
286.72

Answer 1

@Astrophysics

Answer 2

Rate of change is just the slope

Answer 3

SO,

Answer 4

\[rate~of~change = \frac{ f(b)-f(a) }{ b-a }\]

Answer 5

so find f(b) and f(a) where a = 12, and b = 15

Answer 6

\(\bf slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\qquad thus
\\ \quad \\
\cfrac{{\color{blue}{ f(15)}-{\color{blue}{ f(12)}}}}{{\color{red}{ 15-{\color{red}{ 12}}}}}\impliedby \textit{rate of change}\)

Answer 7

For a better understanding

Answer 8

3?

Answer 9

Is that \[f(x) = 0.1(2)^x~~~~\text{or}~~~f(x) = 0.1(2)x\]

Answer 10

I'm assuming it's exponent and no you're wrong

Answer 11

\[f(15) = 0.01(2)^{15}\]

Answer 12

\[f(12) = 0.01(2)^{12}\]

Answer 13

\[rate~of~change = \frac{ 0.01(2)^{15}-0.01(2)^{12} }{ 15-12 }\]

Answer 14

286.72?

Answer 15

No :\, please just use a calculator

Answer 16

You need to divide by 3

Answer 17

i did

Answer 18

wait let me see

Answer 19

What did you get?

Answer 20

i 95.57

Answer 21

Yup!

Answer 22

Make sure you understand what we did though

Answer 23

Once again this is just the slope, the image should show you what it means

Answer 24

oh ok thank you!!! can you help me with two more?

Answer 25

@Sarcasmus

Answer 26

Which of the following options is an equivalent function to f(x) = 3(2)3x?

f(x) = 3(8)x
f(x) = 24x
f(x) = 27(8)x
f(x) = 3(8x)

Answer 27

@muscrat123

Answer 28

@muscrat123

Answer 29

@muscrat123