Can someone help me with this question:

The amount of cocaine in a person's body fluids is modelled by the differential equation:

y'(t)= -ky(t)/(a+y(t)

where A,k are positive constants. For cocaine, A is usually much bigger than y(0). Explain why most folks are happy to say that cocaine concentration decays exponentially.

Not sure how to start

Question

Can someone help me with this question:

The amount of cocaine in a person's body fluids is modelled by the differential equation:

y'(t)= -ky(t)/(a+y(t)

where A,k are positive constants. For cocaine, A is usually much bigger than y(0). Explain why most folks are happy to say that cocaine concentration decays exponentially.

Not sure how to start

anonymous · Answer

this is a seperable DE:

$$\frac{ dy }{ dt } = \frac{ -ky }{ a+y }$$

$$\frac{ (a+y) }{ ky } dy = - dt$$

integrate both sides.

what school do you go to? O_O

anonymous · Answer

easier to look at: $$\frac{ (a+y) }{ y } dy = -kdt$$

anonymous · Answer

let me know if you want the next step(s)

anonymous · Answer

I'd like to see what happens to the left hand side.  Got e^(alogy) . e^y = Ce^-tk
How do we get the y on its own?

anonymous · Answer

I actually don't think you can. my "final answer" looks like:

$$e^yy^a = Ce^{-kt}$$

anonymous · Answer

Ok I'm with you.  Good stuff.

anonymous · Answer

Im studying for a proficiency exam at uiuc and found some old exams online and this was one of them. Im gonna see if i follow but I am a little confused