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Math Help - expoential problem

  1. #1
    Junior Member
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    expoential problem

    Given: There are 7 billion, that is, 7*10^9
    people on Earth. If a bird flu virus starts
    with one person and within 5 days two
    people are infected, then each of those two
    people in 5 days infects 2 people each,
    and so on, how many days before everyone
    on earth is infected?
    Hint: Geometric series and logarithms

    I know this formula....N(t)= 1e(rt) but what would the rate (r) be?
    how do i do this??
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Steph07 View Post
    Given: There are 7 billion, that is, 7*10^9
    people on Earth. If a bird flu virus starts
    with one person and within 5 days two
    people are infected, then each of those two
    people in 5 days infects 2 people each,
    and so on, how many days before everyone
    on earth is infected?
    Hint: Geometric series and logarithms

    I know this formula....N(t)= 1e(rt) but what would the rate (r) be?
    how do i do this??
    The doubling time for number of infections is 5 days, so after t days there are t/5 doubling times and so the number infected is N(t)=N(0)2^{t/5}=2^{t/5} (the first case occurs on day 0)

    CB
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  3. #3
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    so when I get to the ^t/5 how exactly would i solve that?? I'm sry I am a lil slow in this subject
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  4. #4
    Member
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    Auckland, New Zealand
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    You need to solve 2^{t/5} = 7 \times 10^9

    Take logs:
    2^{t/5} = 7 \times 10^9

    \frac{t}{5} \times \ln(2) = \ln(7 \times 10^9)

    t = \frac{5\ln(7\, 000\, 000\, 000)}{\ln(2)}
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