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Homework Help: Exponential Growth

  1. May 25, 2008 #1
    1. The problem statement, all variables and given/known data

    A bacteria culture starts with 1000 bacteria and grows to a population of 7000 after an hour.

    a) Find the size of the population after t hours.
    b) Find the size of the population after 3 hours.
    c) Find the rate of growth of the population after 3 hours.
    d) When will the population reach 10 000?

    2. Relevant equations

    y = yoe[itex]^{kt}[/itex]

    3. The attempt at a solution

    a) y = yoe[itex]^{kt}[/itex]
    7000 = 1000e[itex]^{kt}[/itex]
    7 = e[itex]^{kt}[/itex]
    ln7 = kt
    ln7/t = k (is this it?)

    b) y = yoe[itex]^{kt}[/itex]
    y = 1000e[itex]^{k(2)}[/itex] (am I on the right track?)

    c) I know I have to take the derivative but what do I take the derivative of?

    d) No idea.
    Last edited by a moderator: Jun 2, 2011
  2. jcsd
  3. May 25, 2008 #2


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    You're close. What is the value of t when y = 7000?
  4. Jun 2, 2011 #3
    IM havng a similar problem with N=Ae^(kt)

    N is the number of bcteria in a culture at difrent times (t days) as expressed as a table

    T= 0 ...... 1 .......... 2 ........... 3 ........ 4 ......... 5 .
    N= 10^3. 7.4x10^3. 5.5x10^4. 4x10^5. 3x10^6. 2.2x10^7.

    it asks to envestigate the process with reference to the function above, im confused and needs it explained
  5. Jun 2, 2011 #4


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