How Does Differential Equations Model Drug Distribution in the Bloodstream?

[badtwistoffate]

fluid with 5mg/cm^3 of drug enters bloodsteam at 100cm^3/hr, drug is absorbed by body tissue or otherwise leaves the bloodstream at a rate proportional to the amount present with a rate constant of .4(hr)^-1.

so assuming the drug is always uniformly distrbuted throughout the bloodstream, the differential equation for the amount of the drug that is present at time t is:

What i have done is:
let D(T)=amnt of drug absorbned by the body, at time t (hrs), in mg

so i got dD/dt= rate in - rate out

i have the rate in=100(5) mg/cm^3 or 500 mg/cm^3
and rate out= D(t)/.4

so my equation is dD/dt= 500-D/.4 then i can just you separation of varibles...

what do you all think

 

[HallsofIvy]

Yes, separation of variables will work. You might also note that that is a "linear differential equation with constant coefficients". Either method will work.