Exponential Decay - Example
Problem: A radioactive isotope of iodine decays exponentially. There is 50 mg of the element initially, 35 mg after 4 days.
(a) Find a formula of the form
(b) Find the half-life, , of the isotope.
We know already that our formula is
To find k , we use the fact that after 4 days, that is, at t=4 , there are 35 mg of iodine left. That gives us the following equation
We divide both sides by 50, and take the natural logarithm of both sides. We obtain
Since (from properties of logs), we get
= 0.0891 .
Hence, the formula describing the decay of iodine is