# Math Modeling

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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)

• Math Modeling -

Draw a figure

whole body
intake=loss from body

liver
loss to plasma=gain from plasma

plasma=loss to liver+loss to body-gain 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+1.6mg-1.2mg+1.6mg=0
checks. The system is in equilibrium.

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