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## anonymous one year ago Which of the following options results in a graph that shows exponential decay? f(x) = 0.6(2)x f(x) = 3(0.7)x f(x) = 0.4(1.6)x f(x) = 20(3)x

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1. jim_thompson5910

In general, the exponential function is $\Large f(x) = a*b^x$ The base b determines if you have exponential growth or decay. If 0 < b < 1, then you have exponential decay. If b > 1, then you have exponential growth.

2. jim_thompson5910

For example, the function $\Large f(x) = 33(2.7)^x$ has exponential growth because b = 2.7 is larger than 1.

3. anonymous

Ok so for example f(x) = 3(0.7)to the x power is exponential decay @jim_thompson5910

4. jim_thompson5910

correct

5. jim_thompson5910

since b = 0.7 is between 0 and 1 ie it makes 0 < b < 1 true

6. anonymous

Ok thank you

7. jim_thompson5910

np

8. anonymous

Hey wait can you help me solve another problem? @jim_thompson5910

9. jim_thompson5910

sure

10. jim_thompson5910

go ahead

11. anonymous

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

12. jim_thompson5910

are you able to determine f(2) ?

13. anonymous

Nope that's all the question says

14. jim_thompson5910

replace every x with 2 and evaluate the function

15. anonymous

These are the choices: 1.275 8 10.2 10.24

16. jim_thompson5910

ignore the choices for now

17. jim_thompson5910

$\Large f(x) = 0.01(2)^x$ $\Large f(2) = 0.01(2)^2$ $\Large f(2) = ??$

18. anonymous

0.04

19. jim_thompson5910

yes

20. jim_thompson5910

now evaluate f(10)

21. anonymous

Ok

22. anonymous

I got 1,024

23. jim_thompson5910

you should get something smaller than that, try again

24. jim_thompson5910

$\Large f(x) = 0.01(2)^x$ $\Large f(10) = 0.01(2)^{10}$ $\Large f(10) = ??$

25. anonymous

10.24

26. jim_thompson5910

better

27. anonymous

Is that right

28. jim_thompson5910

Last step: compute $\Large \frac{f(b)-f(a)}{b-a}=\frac{f(10)-f(2)}{10-2} = ??$

29. jim_thompson5910

10.24 is not the answer, but it helps get you there

30. anonymous

Wait is it 8over 8

31. jim_thompson5910

$\Large \frac{f(10)-f(2)}{10-2}=\frac{10.24-0.04}{10-2} = ??$

32. anonymous

Oh ok

33. anonymous

So it 1.275

34. jim_thompson5910

yes

35. anonymous

And that's the right answer

36. jim_thompson5910

yes

37. anonymous

Ok thank you

38. jim_thompson5910

np

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