Math Modeling
posted by Adam on .
Vitamin A is stored primarily in our plasma and our liver. suppose that 40% of the vitamin A in the plasma is filtered out by the kidneys each day and that 30% of the vitamin A in the plasma is absorbed into the liver each day. Also assume that 1% of the vitamin A in the liver is absorbed back into the plasma each day.
(a) how much vitamin A should you ingest each day so that the equilibrium amount of vitamin A in the plasma is 4 mg? Assume all of the vitamin A ingested goes into the plasma.
(b) what is the equilibrium amount of vitamin A in your liver given the answer to part(a)

Draw a figure
whole body
intake=loss from body
liver
loss to plasma=gain from plasma
plasma=loss to liver+loss to bodygain from liver+intake
so you have three equations.
whole body:
intake=.4(4mg)=1.6mg/day
liver
.1L=.3(4mg) or L=12mg
Plasma
.3*4mg+.4*4mg.1L+intake=0
1.2mg+1.6mg1.2mg+1.6mg=0
checks. The system is in equilibrium.