Math
posted by Meli .
A mathematical model for concentration of administered cortisone in humans over a 24hour period uses the function
C= [(D x a) / V(ab)] (e^(bt)e^(at)
where C is the concentration, D is the dose given at time t=0, V is the volume of distribution (volume divided by bioavailability), a is the absorption rate, b is the elimination rate, and t is the time in hours.
a.)What is the value of C at t=0? Explain why this makes sense.
b.)What happens to the concentration as a large amount of time passes? Explain why this makes sense.
c.)The researchers used the values D=500 micrograms, a=8.5, b=0.09, and V=3,700 liters. Use these values and a graphing calculator to estimate when the concentration is greatest.

C(0) = 0
Naturally, at t=0, there has been no drug added
As t>∞, e^bt and e^at >0, so we again have
C(∞) = 0
All the drug has been absorbed or eliminated.
If
C(t) = (500)(8.5)/(3700)(8.50.09) (e^0.09t  e^8.5t)
then max C is at t=0.54 
I assume D x a means D a
I know nothing about medicine but
a) at t = 0, e^0 = 1
so
C(0) = something(11) = 0
It has not had time to be absorbed
after a long time, both e^bt and e^at approach zero so the concentration approaches zero. At first assuming a is much bigger than b the absorption will dominate, but after a long time the elimination rate balances the absorption.
go ahead, do C
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