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Medicine in the Bloodstream

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by

Carlos Cruz

on 19 May 2016

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Transcript of Medicine in the Bloodstream

Amount of Medication left in Body After:
4 hrs: 12-ml

8 hrs: 9-ml

12 hrs: 6.75-ml

16 hrs: 5.0625-ml
Amount of medication after taking second dose
Amount after third and fourth dose, over time?
overall time:
a(n)= a(n-1)*0.75+16

Amount of medication in body during first 16 hrs
Amount of medication (a) left in body after n 4-hr periods
16(3/4)^n=a
The value n, when a=0
0=16(3/4)^n

0=3/4^n
Exponential function has an asympotote at x=0, therefore, a never equals 0
Medicine in the Bloodstream

Limits
What do the continuities mean?
a(n)= 16((3/4)^n)+16
a(1)= 16((3/4)^1)+16
=16(3/4)+16
=12+16
a(1)=28
third dose: (28*0.75) +16=37
fouth dose: (37*0.75)+16= 43.75

Amount of medicine is increasing overtime as number of doses increases.
Lim f(x)=12
x->4-

Lim f(x)=28
x->4+

Lim f(x)=27.75
x->12-

Lim f(x)=43.75
x->12+
16-ml - 16*.25
12 - 12*.25
9 - 9*.25
6 - 6*.25
In real life however, the medication does not forever exist in the person's body
We use the function a(n)= 16((3/4)^n) and add 16-ml from the original dose, adding the n dose plus the original
Every four hours, more medication is added, which causes a spike from the constant rate at which the liver cleans the medication out of the body
There are discontinuities at t= 4, 8, and 12 because the limit from the left and the right are not equal to each other at those points. This is because at theses points, an additional dose is taking, causing an increase in the amount of medication in the patient's body.
When amount eliminated is equal to next dose:
Full transcript