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Thread: Exponential Functions & Logarithms Questions

  1. #1
    Jan 2008

    Exponential Functions & Logarithms Questions

    2 .Assume that the number of viruses present in a sample is modeled by
    the exponential function f(t) = 10t, where t is the elapsed time in

    How would you apply logarithms to determine when the sample will grow
    to 5 billion viruses?

    4. Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double.

    I have the following:
    A = Pe^rt
    A = 600e^(5.64)(t)
    1200 = 600e^(5.64)(t)
    2 = e^(5.64)(t)
    ln(2) = ln(e)^(5.64)(t)
    ln(2) = 5.64t
    (ln(2))/5.64 = t

    Is this correct?

    7. A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another 5 minutes, etc. How long until 100 million computers are infected?
    Last edited by MathGeek06; Feb 12th 2008 at 08:55 AM. Reason: Adding another question
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  2. #2
    Senior Member topher0805's Avatar
    Jan 2008
    1) I assume that you mean $\displaystyle f(t) = 10^t$

    When the sample is grown to 5,000,000,000 we have that:

    $\displaystyle 5000000000 = 10^t$

    Take the log of both sides:

    \log {5000000000} = t\log {10}$

    We know that $\displaystyle \log {10} = 1$, so:

    t = \log {5000000000}$

    Just plug that into your calculator and you have your answer.

    2) Yes that is correct.

    3) Let's call the number of computers infected $\displaystyle I$. We know that after 5 minutes, 20 computers are infected, plus the original 1. We also know that exponentials are of the form:

    $\displaystyle y = ke^ {rt}$

    So we then have:

    $\displaystyle I(t) = 21e^ {4t}$

    To find how long until 100,000,000 computers are infected, simply set the equation equal to 0 and solve for $\displaystyle t$ using the method from question 1.
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