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.

Finding R[0] is easy: R[0] is the initial amount at t = 0 . Indeed, exp(-k*0) = 1 . Hence, R[0] = 50 , and our formula must be

R(t) = 50*exp(-k*t) .

Now we have to find k .