Question

Iodine-131 is used to find leaks in water pipes. It has a half-life span of 8.14 days. Write the exponential decay function for a 200 mg sample. Find the amount of Iodine-131 remaining after 72 days.

Answer 1

decay function:
\[Pe^{-kt}\]
P is initial amount , or 200 mg
solve for "k" by using half-life
set decay function to half the initial amount, using t = 8.14
\[200 e^{-8.14k} = 100\]
\[e^{-8.14k} = \frac{1}{2}\]
\[k = \frac{\ln(1/2)}{-8.14} = \frac{\ln 2}{8.14}\]
Finally plug in t=72 and k value into decay function to get answer