# Alg2

posted by Rock

Radioactive iodine is used to determine the health of the thyroid gland. It decays according to the equation y=ae -0.0856t where t is in days. Find the half-life of this substance. Round to the tenths place.

1. Steve

If you can express the amount as

y = a*2^(-t/n)

then the half-life is n years. That is, as t increases by n, the amount is multiplied by 1/2

ae^-.0856t = a*2^(-t/n)
divide by a and take logs
-.0856t = -t/n ln 2
divide by t

.0856 = ln2/n
n = ln2/.0856 = .6931/.0856 = 8.1

So, the half-life is 8.1 days

check: wikipedia says the half-life is 8.02 days

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