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GOODMAN Group Title

A bacteria culture will grow from 400 to 5000 in 1 1/4 hours. a) Find the constant k for this bacteria using growth formula, y=ne^kt, and write the growth equation. b)Use your equation to predict how much longer it will take the 5000 bacteria to become 15000 bacteria.

  • 2 years ago
  • 2 years ago

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  1. Libniz Group Title
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    \[y=ne^{kt}\]

    • 2 years ago
  2. Libniz Group Title
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    n is beginning y is end

    • 2 years ago
  3. GOODMAN Group Title
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    Correct. Dont know where to start on this problem.

    • 2 years ago
  4. Libniz Group Title
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    so in beginning there was 400

    • 2 years ago
  5. Libniz Group Title
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    so plug in 400 for n

    • 2 years ago
  6. Libniz Group Title
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    plug in what for y?

    • 2 years ago
  7. GOODMAN Group Title
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    5000?

    • 2 years ago
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    yes

    • 2 years ago
  9. Libniz Group Title
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    \[5000=400 e^{kt}\]

    • 2 years ago
  10. Libniz Group Title
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    t represent time , what time do you see there

    • 2 years ago
  11. GOODMAN Group Title
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    t would go in as 1.5

    • 2 years ago
  12. Libniz Group Title
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    1 1/4= 1.25

    • 2 years ago
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    I knew that.

    • 2 years ago
  14. Libniz Group Title
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    let's go with that

    • 2 years ago
  15. GOODMAN Group Title
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    k. so the equation is \[5000=400e ^{k(1.25)}\]

    • 2 years ago
  16. Libniz Group Title
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    yes

    • 2 years ago
  17. Libniz Group Title
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    your job is to find k

    • 2 years ago
  18. GOODMAN Group Title
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    Hmm...take ln of both sides and bring exponent down then solve for k?

    • 2 years ago
  19. Libniz Group Title
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    exactly

    • 2 years ago
  20. GOODMAN Group Title
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    \[\ln(5000)=k(1.25)\ln400e\]

    • 2 years ago
  21. Libniz Group Title
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    not what I would do

    • 2 years ago
  22. GOODMAN Group Title
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    How would you set it up?

    • 2 years ago
  23. Libniz Group Title
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    I would divide both sides by 400 first

    • 2 years ago
  24. GOODMAN Group Title
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    Ohh okay.

    • 2 years ago
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    \[5000/400=e ^{k(1.25)}\]

    • 2 years ago
  26. Libniz Group Title
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    now take ln of both sides

    • 2 years ago
  27. GOODMAN Group Title
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    \[\ln(25/2)=k(1.25)lne\]

    • 2 years ago
  28. GOODMAN Group Title
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    Wouldnt ln and e cancel eachother out though?

    • 2 years ago
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    yes

    • 2 years ago
  30. GOODMAN Group Title
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    So basically, to get k, you would divide ln(25/2) by 1.25?

    • 2 years ago
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    yes

    • 2 years ago
  32. GOODMAN Group Title
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    k=2.02?

    • 2 years ago
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    yes

    • 2 years ago
  34. GOODMAN Group Title
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    lol thanks. so to rewrite the equation, i would just plug everything in?

    • 2 years ago
  35. GOODMAN Group Title
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    \[5000=400e ^{2.02(1.25)}\]

    • 2 years ago
  36. Libniz Group Title
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    close but to be more general you use t instead of specific time

    • 2 years ago
  37. GOODMAN Group Title
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    Ohh okay. So intead of 1.25, just t?

    • 2 years ago
  38. Libniz Group Title
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    \[y=400e ^{2.02(t)}\]

    • 2 years ago
  39. Libniz Group Title
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    that way you can find y for any t value you plug in

    • 2 years ago
  40. GOODMAN Group Title
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    So on b, you would plug n as 5000 and y as 1500?

    • 2 years ago
  41. GOODMAN Group Title
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    *15000

    • 2 years ago
  42. Libniz Group Title
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    exactly , this time you are finding the 't'

    • 2 years ago
  43. GOODMAN Group Title
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    I got 0.5438

    • 2 years ago
  44. GOODMAN Group Title
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    Because you divide by 5000 on both sides. Getting: \[\ln(3)=(2.02)\ln(e)\]

    • 2 years ago
  45. GOODMAN Group Title
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    And then divide by ln(2.02) Did I do it right?

    • 2 years ago
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    yes

    • 2 years ago
  47. GOODMAN Group Title
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    Thank God. lol. But would that be like 5 mins?

    • 2 years ago
  48. Libniz Group Title
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    what?

    • 2 years ago
  49. GOODMAN Group Title
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    .5438

    • 2 years ago
  50. Libniz Group Title
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    yes ,

    • 2 years ago
  51. Libniz Group Title
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    it will take .5438 hours

    • 2 years ago
  52. GOODMAN Group Title
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    okie dokes.

    • 2 years ago
  53. GOODMAN Group Title
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    Thanks youuuu!!

    • 2 years ago
  54. Libniz Group Title
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    nice to meet you

    • 2 years ago
  55. GOODMAN Group Title
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    Nice to meet you too. It was good working with you.

    • 2 years ago
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