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GOODMAN

  • 3 years ago

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.

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  1. Libniz
    • 3 years ago
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    \[y=ne^{kt}\]

  2. Libniz
    • 3 years ago
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    n is beginning y is end

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

  4. Libniz
    • 3 years ago
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    so in beginning there was 400

  5. Libniz
    • 3 years ago
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    so plug in 400 for n

  6. Libniz
    • 3 years ago
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    plug in what for y?

  7. GOODMAN
    • 3 years ago
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    5000?

  8. Libniz
    • 3 years ago
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    yes

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

  10. Libniz
    • 3 years ago
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    t represent time , what time do you see there

  11. GOODMAN
    • 3 years ago
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    t would go in as 1.5

  12. Libniz
    • 3 years ago
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    1 1/4= 1.25

  13. GOODMAN
    • 3 years ago
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    I knew that.

  14. Libniz
    • 3 years ago
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    let's go with that

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

  16. Libniz
    • 3 years ago
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    yes

  17. Libniz
    • 3 years ago
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    your job is to find k

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

  19. Libniz
    • 3 years ago
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    exactly

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

  21. Libniz
    • 3 years ago
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    not what I would do

  22. GOODMAN
    • 3 years ago
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    How would you set it up?

  23. Libniz
    • 3 years ago
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    I would divide both sides by 400 first

  24. GOODMAN
    • 3 years ago
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    Ohh okay.

  25. Libniz
    • 3 years ago
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    \[5000/400=e ^{k(1.25)}\]

  26. Libniz
    • 3 years ago
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    now take ln of both sides

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

  28. GOODMAN
    • 3 years ago
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    Wouldnt ln and e cancel eachother out though?

  29. Libniz
    • 3 years ago
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    yes

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

  31. Libniz
    • 3 years ago
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    yes

  32. GOODMAN
    • 3 years ago
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    k=2.02?

  33. Libniz
    • 3 years ago
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    yes

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

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

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

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

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

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

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

  41. GOODMAN
    • 3 years ago
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    *15000

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

  43. GOODMAN
    • 3 years ago
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    I got 0.5438

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

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

  46. Libniz
    • 3 years ago
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    yes

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

  48. Libniz
    • 3 years ago
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    what?

  49. GOODMAN
    • 3 years ago
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    .5438

  50. Libniz
    • 3 years ago
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    yes ,

  51. Libniz
    • 3 years ago
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    it will take .5438 hours

  52. GOODMAN
    • 3 years ago
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    okie dokes.

  53. GOODMAN
    • 3 years ago
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    Thanks youuuu!!

  54. Libniz
    • 3 years ago
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    nice to meet you

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

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