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anonymous

  • one year ago

Jake is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = 2x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength Pascals.

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  1. anonymous
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    x is the length, what is f(x)?

  3. anonymous
    • one year ago
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    y?

  4. jim_thompson5910
    • one year ago
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    in terms of the word problem

  5. anonymous
    • one year ago
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    the strength in terms of the length

  6. jim_thompson5910
    • one year ago
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    yes, x = length, f(x) = strength

  7. jim_thompson5910
    • one year ago
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    so when they say `strength is 8 Pascals.` we can replace `f(x)` with `8`

  8. anonymous
    • one year ago
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    8=2^x

  9. jim_thompson5910
    • one year ago
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    now convert that to a log equation

  10. anonymous
    • one year ago
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    Ok:) is it log 2x =8?

  11. jim_thompson5910
    • one year ago
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    I think you mean \[\Large \log_2(x) = 8\] right? you're close but not quite there

  12. anonymous
    • one year ago
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    yes! Something along those lines

  13. jim_thompson5910
    • one year ago
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    you'll use the rule \[\Large b^x = y \ \ \implies \ \ \log_b(y) = x\]

  14. anonymous
    • one year ago
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    Ok thank-you :)!!

  15. anonymous
    • one year ago
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    what about the 8 pascals?

  16. jim_thompson5910
    • one year ago
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    how would you use that rule to rewrite \[\Large 2^x = 8\]

  17. anonymous
    • one year ago
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    Look at base b^x=y as if it were 2^x=8

  18. anonymous
    • one year ago
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    Now look at the log equation and replace each variable with the corresponding one.

  19. jim_thompson5910
    • one year ago
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    yeah so b = 2 and y = 8

  20. anonymous
    • one year ago
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    That's it right?

  21. jim_thompson5910
    • one year ago
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    what log equation do you have now

  22. anonymous
    • one year ago
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    2^x = 8 means log(base 2) 8 = x

  23. jim_thompson5910
    • one year ago
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    good

  24. anonymous
    • one year ago
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    That's it then?

  25. jim_thompson5910
    • one year ago
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    yeah \[\Large 2^x = 8\] turns into \[\Large \log_2(8) = x\]

  26. anonymous
    • one year ago
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    Thank you so much~~!!

  27. anonymous
    • one year ago
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    I have one more?

  28. jim_thompson5910
    • one year ago
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    go ahead

  29. jim_thompson5910
    • one year ago
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    what are your thoughts?

  30. anonymous
    • one year ago
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    it's suppose to be 50^x. Sorry!

  31. anonymous
    • one year ago
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    I would tell her to convert it. I dont know which formula to use now though

  32. jim_thompson5910
    • one year ago
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    you'd use the one I just posted. The rule going from exponential to log

  33. anonymous
    • one year ago
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    Ok. Lemme try it

  34. anonymous
    • one year ago
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    log 50 (17)=x

  35. jim_thompson5910
    • one year ago
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    yes, \[\Large \log_{50}(17) = x\]

  36. anonymous
    • one year ago
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    That's it? It was that simple?

  37. jim_thompson5910
    • one year ago
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    here is a pic that has an alternate route http://ashikmdigitalportfolio.weebly.com/uploads/1/9/2/5/19253115/8805020_orig.jpg?146 either method gets the same answer

  38. anonymous
    • one year ago
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    Thank you!!!

  39. anonymous
    • one year ago
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    Can I ask one last question? Pleasee?

  40. jim_thompson5910
    • one year ago
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    sure

  41. anonymous
    • one year ago
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    Shannon manages a small zoo and she has been analyzing the attendance data. Shannon finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 3x. Shannon also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by f(x) = −x + 4. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.

  42. anonymous
    • one year ago
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    Ty!

  43. jim_thompson5910
    • one year ago
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    it says `The graph of the two functions is below` where do the two functions cross?

  44. anonymous
    • one year ago
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    oh hold on! I can graph it

  45. jim_thompson5910
    • one year ago
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    looks good

  46. jim_thompson5910
    • one year ago
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    where do the two functions cross?

  47. anonymous
    • one year ago
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    at (1,3)

  48. jim_thompson5910
    • one year ago
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    what does that point mean?

  49. anonymous
    • one year ago
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    It is the solution?

  50. jim_thompson5910
    • one year ago
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    it's the solution to the system, yes but what does that solution mean in terms of the word problem?

  51. anonymous
    • one year ago
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    The number of people who leave the park early due to the temperature?

  52. jim_thompson5910
    • one year ago
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    let's go back to each function one by one f(x) = 3^x what is x? what is f(x)?

  53. anonymous
    • one year ago
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    umm the increase in temperature for f(x)?

  54. jim_thompson5910
    • one year ago
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    for f(x) = 3^x x = temperature f(x) = number of visitors

  55. jim_thompson5910
    • one year ago
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    how about g(x) = -x+4 ?

  56. anonymous
    • one year ago
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    -x=temperature or people leaving?

  57. jim_thompson5910
    • one year ago
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    x looks like the change in temp

  58. anonymous
    • one year ago
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    yes

  59. anonymous
    • one year ago
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    hmm..is that when the temperature and # of people are equal?

  60. anonymous
    • one year ago
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    Wait! NVM haha

  61. jim_thompson5910
    • one year ago
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    so what I'm thinking is that when x = 1, the temperature change is 1 degree so as the temp increases by 1, the number of visitors is 3 (maybe 3 thousand or something) also, when x = 1, the number of people who leave early is 3 (thousand?) this problem is a bit odd

  62. anonymous
    • one year ago
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    I know right? Ugh!!! So, would (1,3) mean that that's the temp. needed to have the most visitors?

  63. jim_thompson5910
    • one year ago
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    maybe it's when the temp change is +1, then the number of visitors equals the number of people who leave early

  64. jim_thompson5910
    • one year ago
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    what's strange is that I don't see how you can get more visitors growing forever if it's like 100+ degrees. If anything, the attendance would go down

  65. anonymous
    • one year ago
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    Oh! I didn't look at it that way! That is strange.

  66. anonymous
    • one year ago
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    It's a poorly worded question tbh

  67. jim_thompson5910
    • one year ago
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    yeah I agree

  68. anonymous
    • one year ago
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    i'm going to go with your answer :)

  69. anonymous
    • one year ago
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    Thanks so much for all your help today!!! You're awesome :D

  70. jim_thompson5910
    • one year ago
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    sure thing

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