Exponential problem: caffeine dosage

1. Mar 23, 2013

jackscholar

If the concentration of caffeine in a system at any given time is given by the equation
y(t)=De^-kt
where dy/dt=-kt is the clearence rate (re-arranged and integrated to form the above equation) and the concentration of caffeine in the system at t=0 is D, then calculate k if:
After one hour, 25% of the caffein has been cleared.

I know that y(60)= 3D/4 or three quarters of D
so how do I re-arrange to get k?

2. Mar 23, 2013

Dick

y(60)=De^(-k*60). That's equal to 3D/4. It shouldn't be too hard to solve for k if you use a log, is it?

3. Mar 23, 2013

jackscholar

OH! I see now. Just subtitute in 3/4D for y(60) then divide by D, take ln of both sides and divide by negative 60. Thank you!

4. Mar 23, 2013

Ray Vickson

Note: dy/dt is NOT equal to -kt; it is equal to -ky.