anonymous
  • anonymous
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
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Astrophysics
  • Astrophysics
Rate of change is just the slope
anonymous
  • anonymous
SO,

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Astrophysics
  • Astrophysics
\[rate~of~change = \frac{ f(b)-f(a) }{ b-a }\]
Astrophysics
  • Astrophysics
so find f(b) and f(a) where a = 12, and b = 15
jdoe0001
  • jdoe0001
\(\bf slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\qquad thus \\ \quad \\ \cfrac{{\color{blue}{ f(15)}-{\color{blue}{ f(12)}}}}{{\color{red}{ 15-{\color{red}{ 12}}}}}\impliedby \textit{rate of change}\)
Astrophysics
  • Astrophysics
|dw:1436397137594:dw|
Astrophysics
  • Astrophysics
For a better understanding
anonymous
  • anonymous
3?
Astrophysics
  • Astrophysics
Is that \[f(x) = 0.1(2)^x~~~~\text{or}~~~f(x) = 0.1(2)x\]
Astrophysics
  • Astrophysics
I'm assuming it's exponent and no you're wrong
Astrophysics
  • Astrophysics
\[f(15) = 0.01(2)^{15}\]
Astrophysics
  • Astrophysics
\[f(12) = 0.01(2)^{12}\]
Astrophysics
  • Astrophysics
\[rate~of~change = \frac{ 0.01(2)^{15}-0.01(2)^{12} }{ 15-12 }\]
anonymous
  • anonymous
286.72?
Astrophysics
  • Astrophysics
No :\, please just use a calculator
Astrophysics
  • Astrophysics
You need to divide by 3
anonymous
  • anonymous
i did
anonymous
  • anonymous
wait let me see
Astrophysics
  • Astrophysics
What did you get?
anonymous
  • anonymous
i 95.57
Astrophysics
  • Astrophysics
Yup!
Astrophysics
  • Astrophysics
Make sure you understand what we did though
Astrophysics
  • Astrophysics
Once again this is just the slope, the image should show you what it means |dw:1436398295490:dw|
anonymous
  • anonymous
oh ok thank you!!! can you help me with two more?
anonymous
  • anonymous
anonymous
  • anonymous
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)
anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous

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