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Math Help - exponential function

  1. #1
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    exponential function

    1000000 viruses are reproducing exponentially with a rate of 160% in four hours. At the same time, the body is eliminating the viruses constantly at 50000 per hour. What would be the function giving the virus population at a given time?

    k must be ln(1,6)/4, because
    e^k*4 must be 1,6.
    the differential equation for exponential growth is
    dP/dt = Po * e ^(kt) * k

    WHAT AM I GOING TO DO ABOUT THE ELIMINATION RATE PLEASE HELP!!!
    Last edited by nrslmz; December 18th 2008 at 08:43 AM. Reason: more info
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  2. #2
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    This is what i thought but i maybe wrong. What do you think ?

    v(t) = 1000000^1.6(t/4) - 50000t
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  3. #3
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    Yes, I have tried that one. I think that is incorrect because while the viruses grow exponentially, the elimination is constant. Each time the viruses reproduce it takes out 50000, changing the initial virus population. If you do that, I think (BUT NOT KNOW) multiplicating the initial virus number by e^k t times won't work.
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  4. #4
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    Ok noted. Anyway previous post thread updated due to type should be - 5000t instead of + 5000t. Will let you know if i work something out.
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  5. #5
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    Quote Originally Posted by nrslmz View Post
    1000000 viruses are reproducing exponentially with a rate of 160% in four hours. At the same time, the body is eliminating the viruses constantly at 50000 per hour. What would be the function giving the virus population at a given time?

    k must be ln(1,6)/4, because
    e^k*4 must be 1,6.
    the differential equation for exponential growth is
    dP/dt = Po * e ^(kt) * k

    WHAT AM I GOING TO DO ABOUT THE ELIMINATION RATE PLEASE HELP!!!
    Hi nrslmz,

    This looks like an interesting question. I am probably trying the long way, but this is what I have worked out:

    When t = 0, P_0=1000000

    When t = 1, P_1=P_0(1.6)^{\frac{1}{4}}-50000
    =1000000(1.6)^{\frac{1}{4}}-50000

    When t = 2, P_2=P_1(1.6)^{\frac{2}{4}}-50000
    =[1000000(1.6)^{\frac{1}{4}}-50000](1.6)^{\frac{2}{4}}-50000
    =1000000(1.6)^{\frac{1}{4}+\frac{2}{4}}-50000(1.6)^{\frac{2}{4}}-50000


    When t = 3, P_3=P_2(1.6)^{\frac{3}{4}}-50000
    =[1000000(1.6)^{\frac{1}{4}+\frac{2}{4}}-50000(1.6)^{\frac{2}{4}}-50000](1.6)^{\frac{3}{4}}-50000
    =1000000(1.6)^{\frac{1}{4}+\frac{2}{4}+\frac{3}{4}  }-50000(1.6)^{\frac{2}{4}+\frac{3}{4}}-50000(1.6)^{\frac{3}{4}}-50000


    When t = 4, P_4=P_3(1.6)^{\frac{4}{4}}-50000
    =[1000000(1.6)^{\frac{1}{4}+\frac{2}{4}+\frac{3}{4}}-50000(1.6)^{\frac{2}{4}+\frac{3}{4}}-50000(1.6)^{\frac{3}{4}}-50000](1.6)^{\frac{4}{4}}-50000
    =1000000(1.6)^{\frac{1}{4}+\frac{2}{4}+\frac{3}{4}  +\frac{4}{4}}-50000(1.6)^{\frac{2}{4}+\frac{3}{4}+\frac{4}{4}}-50000(1.6)^{\frac{3}{4}+\frac{4}{4}}-50000(1.6)^{\frac{4}{4}}-50000

    Hope that help you start.
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