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anonymous

  • 5 years ago

A quantity P obeys the exponential growth law P(t)=Ce^kt (t in years). Find the formula for P(t), assuming that the doubling time is 7 years & P(0)=100.

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  1. anonymous
    • 5 years ago
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    P(0) = 100 means 100 = C*1, so C = 100

  2. anonymous
    • 5 years ago
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    Would k = 7 because that's the doubling time ?

  3. anonymous
    • 5 years ago
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    wouldn't it mean that e^(k*7) = 2? since after 7 years, you have multiplied by 2?

  4. anonymous
    • 5 years ago
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    then ln2 = k*7, and k = (ln2)/7 Does that make sense?

  5. anonymous
    • 5 years ago
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    then when t = 14, e^((ln2/7)*14) = e^2ln2 = e^ln4 = 4 I think that's it. take your "doubling time and make it into a fraction of ln2/(doubling time) =k

  6. anonymous
    • 5 years ago
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    I kind of get it, let me work it out on paper. Thanks!

  7. anonymous
    • 5 years ago
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    hello again, the formula would be P(t) = 100e^(t*ln2/7)

  8. anonymous
    • 5 years ago
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    Why wouldn't it be 4 ?

  9. anonymous
    • 5 years ago
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    Oh , nevermind ! I got it . Thanks again !

  10. anonymous
    • 5 years ago
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    no, the 4 was just to test it because I haven't done these in a while

  11. anonymous
    • 5 years ago
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    Gotcha .

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