# Thread: Exponential with E^-kt, solving for t

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

I hope this image will show through nicely:

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.

2. ## Re: Exponential with E^-kt, solving for t

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

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.
$\displaystyle \ln(e) = 1$

3. ## Re: Exponential with E^-kt, solving for t

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

Do you see that $\displaystyle 1=100e^{-kt}$ is the same as $\displaystyle e^{kt}=100~?$

4. ## Re: Exponential with E^-kt, solving for t

I don't see that yet

5. ## Re: Exponential with E^-kt, solving for t

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

Can you solve it now for $\displaystyle t$?