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Math Help - Exponential Functions/Logs Questions -- Help!

  1. #1
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    Exponential Functions/Logs Questions -- Help!

    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
    minutes.

    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?
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  2. #2
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    Quote Originally Posted by MathGeek06 View Post
    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
    minutes.

    How would you apply logarithms to determine when the sample will grow
    to 5 billion viruses?
    I assume you mean f(t)=10^t

    Solve 10^t=5 billion

    Remember log(10^t)=tlog(10)

    Using base 10 you get t=log(5 billion)

    Quote Originally Posted by MathGeek06 View Post
    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.
    Try 1200=600x  1.0564^t

    Quote Originally Posted by MathGeek06 View Post
    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?
    1+20+400..... This is a geometric series.
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  3. #3
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    Thanks a tutor!

    Is it possible that someone can be more specific in helping me answer the last question about the computer virus. I see that it is a geometric series, but I am still not sure how to go about getting the answer to the question.
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  4. #4
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    first term a=1
    common ratio r=20

    Sum of first n terms S_n=\frac{a(1-r^n)}{1-r}

    In this case 10^8=\frac{1-20^n}{1-20}

    Solve that to get your answer.
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