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Math Help - Population

  1. #1
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    Population

    how would someone work this out???

    In a bacteria growing experiment, a biologist observes that the number of bacteria in a certain culture triples every 4 hours. After 12 hours, it is estimated that there are 1 million bacteria in the culture.
    a. How many bacteria were present initially
    b. What is the doubling time for the bacteria population?

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by runner07 View Post
    how would someone work this out???

    In a bacteria growing experiment, a biologist observes that the number of bacteria in a certain culture triples every 4 hours. After 12 hours, it is estimated that there are 1 million bacteria in the culture.
    a. How many bacteria were present initially
    b. What is the doubling time for the bacteria population?

    We use the exponential growth formula here.

    P(t) = P_0e^{rt}

    where P(t) is the population at time t, P_0 is the initial population, r is the rate of growth, and t is time.

    (a)
    we are told that after 4 hours, the population triples. so if we start with P_0 at t=0, we will have 3P_0 when t=4. So let's plug those values into our equation.

    3P_0 = P_0e^{4r}

    \Rightarrow 3 = e^{4r}

    \Rightarrow r = \frac {\ln 3}{4}

    So we have, P(t) = P_0e^{\frac {\ln 3}{4}t}

    we are also told that when t=12, the population is 1000000

    so we have:

    1000000 = P_0e^{\frac {\ln 3}{4}(12)}

    now solve for P_0


    once you find P_0, you will have the equation that models this growth, part (b) won't be difficult after that. So find P_0 and try part (b) and we'll see how far you get


    EDIT: This is my 33th post!!!
    Last edited by Jhevon; September 7th 2007 at 01:55 PM.
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