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BIO ALEVEL-calculation

Colostrum is the milk that kittens drink from their mother immediately after they
are born. Maternal antibodies against FPV can be passed to the kittens from the
mother in the colostrum.
The level of antibodies in the kittens halves every 10 days.
These antibodies protect the kittens from FPV for approximately seven weeks.
Estimate the proportion of antibodies remaining in the kittens after seven
weeks.
Original post by MARYAM1234567
Colostrum is the milk that kittens drink from their mother immediately after they
are born. Maternal antibodies against FPV can be passed to the kittens from the
mother in the colostrum.
The level of antibodies in the kittens halves every 10 days.
These antibodies protect the kittens from FPV for approximately seven weeks.
Estimate the proportion of antibodies remaining in the kittens after seven
weeks.

At t=0, the level of antibodies is A0A_0
We know that A halves every 10 days
7 weeks = 49 days
So A will halve nearly 5 times
A0A02A04...A_0 \rightarrow \dfrac{A_0}{2} \rightarrow \dfrac{A_0}{4} \rightarrow ...
i.e A0×125A_0 \times \dfrac{1}{2}^5
so proportion left = 132A0A0=132 \dfrac{ \dfrac{1}{32} A_0}{A_0} = \dfrac{1}{32}
we approximate 0.03125
this is good enough

Exact value:
number of half lives = 49/10 = 4.9
hence proportion = 24.92^{-4.9} = 0.0335
The proportion after n half lives is 2n2^{-n}
(edited 5 years ago)
THANKS!!!

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