**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.

Finding is easy: is the initial amount at . Indeed, . Hence, , and our formula must be

.

Now we have to find
*k*
.