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Math Help - Questions part 1

  1. #1
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    Questions part 1

    1) The number of yeast cells in a laboratory culture increases rapidly at first but levels off eventually. The population is modeled by the function below, where t is measured in hours. At time t = 0 the population is 10 cells and is increasing at a rate of 2 cells/hour.

    a = ?
    b = ?

    According to this model, at what number of cell does the yeast population stabilize in the long run?

    2) Suppose that a population of bacteria triples every hour and starts with 800 bacteria.

    (a) Find an expression for the number n of bacteria after t hours.

    f(t) = (800)3^t <- I did that already

    f'(2.5) = ?
    Last edited by mr fantastic; October 8th 2009 at 04:58 PM. Reason: Questions moved to new thread
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  2. #2
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    Quote Originally Posted by CFem View Post
    1) The number of yeast cells in a laboratory culture increases rapidly at first but levels off eventually. The population is modeled by the function below, where t is measured in hours. At time t = 0 the population is 10 cells and is increasing at a rate of 2 cells/hour.

    a = ?
    b = ?

    According to this model, at what number of cell does the yeast population stabilize in the long run?


    t = 0 the population is 10 cells and is increasing at a rate of 2 cells/hour.

    Therefore you have the data points (0,10) and (1,12)

    Find a and b by using the data given.

    after you have a and b, take the limit of the function for t \rightarrow \infty
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  3. #3
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    When you say solve for a and be using the information given, does that mean like a system of equations?

    Because I did that and solved for a and got the wrong answer. Unless there's an easier way to do it? .-.
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  4. #4
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    Yes, that's exactly what that means. You have f(t)= \frac{a}{1+be^{-0.3t}} and you know that f(0)= 10 and f'(0)= 2. f(0)= 10 gives you the equation \frac{a}{1+ b}= 10. To use f'(0)= 2, you will need to differentiate f(x). You might find it simplest to write f(t) as a(1+ be^{-0.3t})^{-1} and using the chain rule. Or else use the quotient rule.
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