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A bacteria culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour the population has increased to 360 cells.
(a) Find the number of bacteria after t hours.
(b) Find the number of bacteria after 4 hours.
I found part a, P(t)= 200e^(1.2*t)
but when I solve part b it's different than the model answer!

  • Calculus -

    I found the following:
    360 = 200 e^(.5k) , where k is a constant
    1.8 = e^(.5k)
    ln 1.8 = .5k lne
    .5k = ln 1.8
    k = 1.1755733..

    so Number = 200 e^(1.755733t)
    when t=4
    number = 200 e^4.702293..
    = 22039.9
    or appr 22040 bacteria

    It looks like you rounded of the value of k too early.
    Since you are using a calculator anyway, why round off any numbers at all ?
    Just use them the way they appear on your device, so there is no need to re-enter any numbers.
    I also use the memory locations of my calculators to store any intermediate results.
    If we use your value of k = 1.2
    Number = 200 e^(4*1.2) = appr 24302 which is significantly different from the answer I got.

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