posted by Rock on .
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.
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