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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
    • one year ago
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    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
    • one year ago
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    For example, the function \[\Large f(x) = 33(2.7)^x\] has exponential growth because b = 2.7 is larger than 1.

  3. anonymous
    • one year ago
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    Ok so for example f(x) = 3(0.7)to the x power is exponential decay @jim_thompson5910

  4. jim_thompson5910
    • one year ago
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    correct

  5. jim_thompson5910
    • one year ago
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    since b = 0.7 is between 0 and 1 ie it makes `0 < b < 1` true

  6. anonymous
    • one year ago
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    Ok thank you

  7. jim_thompson5910
    • one year ago
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    np

  8. anonymous
    • one year ago
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    Hey wait can you help me solve another problem? @jim_thompson5910

  9. jim_thompson5910
    • one year ago
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    sure

  10. jim_thompson5910
    • one year ago
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    go ahead

  11. anonymous
    • one year ago
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    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
    • one year ago
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    are you able to determine f(2) ?

  13. anonymous
    • one year ago
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    Nope that's all the question says

  14. jim_thompson5910
    • one year ago
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    replace every x with 2 and evaluate the function

  15. anonymous
    • one year ago
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    These are the choices: 1.275 8 10.2 10.24

  16. jim_thompson5910
    • one year ago
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    ignore the choices for now

  17. jim_thompson5910
    • one year ago
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    \[\Large f(x) = 0.01(2)^x\] \[\Large f(2) = 0.01(2)^2\] \[\Large f(2) = ??\]

  18. anonymous
    • one year ago
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    0.04

  19. jim_thompson5910
    • one year ago
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    yes

  20. jim_thompson5910
    • one year ago
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    now evaluate f(10)

  21. anonymous
    • one year ago
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    Ok

  22. anonymous
    • one year ago
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    I got 1,024

  23. jim_thompson5910
    • one year ago
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    you should get something smaller than that, try again

  24. jim_thompson5910
    • one year ago
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    \[\Large f(x) = 0.01(2)^x\] \[\Large f(10) = 0.01(2)^{10}\] \[\Large f(10) = ??\]

  25. anonymous
    • one year ago
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    10.24

  26. jim_thompson5910
    • one year ago
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    better

  27. anonymous
    • one year ago
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    Is that right

  28. jim_thompson5910
    • one year ago
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    Last step: compute \[\Large \frac{f(b)-f(a)}{b-a}=\frac{f(10)-f(2)}{10-2} = ??\]

  29. jim_thompson5910
    • one year ago
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    10.24 is not the answer, but it helps get you there

  30. anonymous
    • one year ago
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    Wait is it 8over 8

  31. jim_thompson5910
    • one year ago
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    \[\Large \frac{f(10)-f(2)}{10-2}=\frac{10.24-0.04}{10-2} = ??\]

  32. anonymous
    • one year ago
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    Oh ok

  33. anonymous
    • one year ago
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    So it 1.275

  34. jim_thompson5910
    • one year ago
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    yes

  35. anonymous
    • one year ago
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    And that's the right answer

  36. jim_thompson5910
    • one year ago
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    yes

  37. anonymous
    • one year ago
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    Ok thank you

  38. jim_thompson5910
    • one year ago
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    np

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