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

R(t) = R[0]*exp(-k*t)

       that models the process of decay.

      (b) Find the half-life, t[h] , of the isotope.

As in every applied problem, first you have to define your variables and their units. Let R(t) 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

R(t) = R[0]*exp(-k*t)

describing the amount left as time changes, we need to find the constants R[0] and   k .