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Math Help - Exponential with E^-kt, solving for t

  1. #1
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    Exponential with E^-kt, solving for t

    I hope this image will show through nicely:

    Exponential with E^-kt, solving for t-solve-t.gif


    I've done so far:

    1/100 = e^-kt
    ln (1/100) = ln e^-kt
    -kt = ln(1/100)/ln e
    t = ln(1/100)/ln e * -k

    Am I right? Maybe ln e needs to be cancelled to something? Please help me out here.
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  2. #2
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    Re: Exponential with E^-kt, solving for t

    Quote Originally Posted by Aluminium View Post
    I hope this image will show through nicely:

    Click image for larger version. 

Name:	solve for t.gif 
Views:	28 
Size:	1.4 KB 
ID:	22010


    I've done so far:

    1/100 = e^-kt
    ln (1/100) = ln e^-kt
    -kt = ln(1/100)/ln e
    t = ln(1/100)/ln e * -k

    Am I right? Maybe ln e needs to be cancelled to something? Please help me out here.
    \ln(e) = 1
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  3. #3
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    Re: Exponential with E^-kt, solving for t

    Quote Originally Posted by Aluminium View Post
    I hope this image will show through nicely:

    Click image for larger version. 

Name:	solve for t.gif 
Views:	28 
Size:	1.4 KB 
ID:	22010
    Do you see that 1=100e^{-kt} is the same as e^{kt}=100~?
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  4. #4
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    Re: Exponential with E^-kt, solving for t

    I don't see that yet
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Exponential with E^-kt, solving for t

    Well:
    1=100\cdot e^{-kt} \Leftrightarrow \frac{1}{100}=e^{-kt} \Leftrightarrow 100=\frac{1}{e^{-kt}} \Leftrightarrow 100=e^{kt}

    Can you solve it now for t?
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