Radioactive decay Radioactive substances decay at a rate that is proportional to the amount present. Thus, if 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.