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Math Help - Exponential and Logarithmic models

  1. #1
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    Exponential and Logarithmic models

    Here is the question that I do not understand and I don't know which model I am going to use:

    HIV/AIDS. In 2003, an estimated 1 million people had been infected with HIV in the united states. If the infection rate increases at an annual rate of 2.5% a year compounding continuously, how many Americans will be infected with the HIV virus by 2010?

    Can you help please. thank you!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Anemori View Post
    Here is the question that I do not understand and I don't know which model I am going to use:

    HIV/AIDS. In 2003, an estimated 1 million people had been infected with HIV in the united states. If the infection rate increases at an annual rate of 2.5% a year compounding continuously, how many Americans will be infected with the HIV virus by 2010?

    Can you help please. thank you!
    "compounded continuously" (without harvesting) means you should use the Malthusian model

    So let P(t) be the number of Americans infected at time t, P_0 be the initial amount infected, and r be the rate of infection written as a decimal, then you have

    P(t) = P_0e^{rt}

    Can you finish up?
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    "compounded continuously" (without harvesting) means you should use the Malthusian model

    So let P(t) be the number of Americans infected at time t, P_0 be the initial amount infected, and r be the rate of infection written as a decimal, then you have

    P(t) = P_0e^{rt}

    Can you finish up?

     Let P_0=1000000
    Let r = 2.5% = 0.025
    Let t= 2003 - 2010
    P(t) = ?

    P(t) = 1000000e^{0.025(7)}
    P(t) = 1191246.217 people

    Is this right?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Anemori View Post
     Let P_0=1000000
    Let r = 2.5% = 0.025
    Let t= 2003 - 2010
    P(t) = ?

    P(t) = 1000000e^{0.025(7)}
    P(t) = 1191246.217 people

    Is this right?
    yes, but i'd round it off to a whole number since we're talking about people.
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