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 halflife of this substance. Round to the tenths place.

Steve
If you can express the amount as
y = a*2^(t/n)
then the halflife 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 halflife is 8.1 days
check: wikipedia says the halflife is 8.02 days
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