Radioactive substances decay at a rate that is proportional to the amount present. Thus, if k is a constant and the amount present is x, the decay rate is dx/dt = kx (t in hours) This means that the relationship between the time and the amount of substance present can be found by evaluating the integral t = ∫ dx/kx
(a) Evaluate the integral to find the relationship.
(b) Use properties of logarithms and exponential functions to write x as a function of t.