## anonymous one year ago 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

1. anonymous

@Astrophysics

2. Astrophysics

Rate of change is just the slope

3. anonymous

SO,

4. Astrophysics

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

5. Astrophysics

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

6. anonymous

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

7. Astrophysics

|dw:1436397137594:dw|

8. Astrophysics

For a better understanding

9. anonymous

3?

10. Astrophysics

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

11. Astrophysics

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

12. Astrophysics

$f(15) = 0.01(2)^{15}$

13. Astrophysics

$f(12) = 0.01(2)^{12}$

14. Astrophysics

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

15. anonymous

286.72?

16. Astrophysics

No :\, please just use a calculator

17. Astrophysics

You need to divide by 3

18. anonymous

i did

19. anonymous

wait let me see

20. Astrophysics

What did you get?

21. anonymous

i 95.57

22. Astrophysics

Yup!

23. Astrophysics

Make sure you understand what we did though

24. Astrophysics

Once again this is just the slope, the image should show you what it means |dw:1436398295490:dw|

25. anonymous

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

26. anonymous

@Sarcasmus

27. 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)

28. anonymous

@muscrat123

29. anonymous

@muscrat123

30. anonymous

@muscrat123