**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

that models the process of decay.

(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

.