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The number of bacteria in a culture is modeled by

n(t)=1710e071t
(a) The initial number of bacteria is
(b) The relative rate of growth of this bacterium population is
(c) The number of bacteria after 3 hours is
(d) After how many hours will the number of bacteria reach 10,000?
Your answer is

I got the A=1710
B=?
c=14389
D=?
I keep getting b and d wrong any suggestions. thanks in advance!

  • math -

    a. ok.

    b.

    c. ok.

    d. 1710*e^0.71t = 10,000
    e^0.71t = 10,000 / 1710 = 5.85
    0.71t*Lne = Ln5.85
    Divide both sides by Lne:
    0.71t = Ln5.85 / Lne = 1.7664
    t = 1.7664 / 0.71 = 2.49 Hours.

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