SOLUTION: 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

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 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       Log On


   

Question 182244This question is from textbook
: 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
i dont understand all you are given is the exponent of -0.0856 This question is from textbook

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
At time t=0, you have "a" units of iodine since
y=a%2Ae%5E%28-0.0856%280%29%29=a%2A%281%29=a
Half life is the time it takes to reach 1/2 of your original amount.
Since you started with "a" units, how long will it take to get to "a/2" units?
a%2F2=a%2Ae%5E%28-0.0856t%29
1%2F2=e%5E%28-0.0856t%29
ln%281%2F2%29=-0.0856t
t=ln%281%2F2%29%2F%28-0.0856%29
or approximately
t=%28-0.693%29%2F%28-0.0856%29
t=8.1
It takes 8.1 time units to get to 1/2 of the original amount of iodine.
The time unit is dependent on how 0.0856 is originally defined.