**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.

As in every applied problem, first you have to define your variables and their units. Let
denote the amount of iodine left, in mg, after time
*t*
. Time
*t*
is measured in days after the initial moment when we began observing the isotope.
To find the formula

describing the amount left as time changes, we need to find the constants
and
*k*
.