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Math Help - Differentiating an exponential function..

  1. #1
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    Differentiating an exponential function..

    P(t) = 50(2)^(t/2)
    Last edited by kmjt; May 3rd 2010 at 09:04 PM.
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  2. #2
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    {\mathrm{d}\over\mathrm{d}t}(50\cdot 2^{t/2}) = 50 {\mathrm{d}\over\mathrm{d}t} (2^{t/2}) = 50{\mathrm{d}\over\mathrm{d}t} (e^{\log 2})^{t/2} = 50{\mathrm{d}\over\mathrm{d}t} e^{\frac12t\log 2} = 50 e^{\frac12t\log 2} {\mathrm{d}\over\mathrm{d}t}(\frac12 t \log 2) = 50\cdot 2^{t/2} \cdot \frac{\log 2}2 = 25\cdot 2^{t/2}\log 2
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  3. #3
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    Hmm, part of what i'm doing asks me to find the slope at 7 days; the answer is 196. However when I sub in 7 for t this is what I get:

    P(t) = 50(2)^(t/2)
    P'(t) = 25(2^(t/2)log2)
    P'(7) = 25(2^(7/2)log2)
    = 25((11.3137085)(0.3010299957)) *2^(7/2)=11.3137085, log2=0.3010299957
    =25(3.40576562)
    =85.14414051

    The answer is 196, so i'm assuming I did something wrong. Perhaps is your derivative wrong, or did I do something wrong with my calculations?
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  4. #4
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    Oh, I use log for the natural logarithm, so \log 2 \approx 0.693. You probably write it \ln 2.
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  5. #5
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    In that case it makes sense So for my derivative, I would just write ln2 throughout all of the steps instead of log2?
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  6. #6
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    Yea, I guess.
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