#Q(t) = Q_(o)e^(-kt)# may be used to model radioactive decay. #Q# represents the quantity remaining after years; #k# is the decay constant, 0.00011. How long, in years, will it take for a quantity of plutonium-240 to decay to 25% of its original amount?
The initial quantity at t = 0 is:
The amount left after t years is one quarter of the initial:
Substitute this expression into the function and the
Take the natural log of both sides, this is the inverse operation of
According to nuclear-power.net, the half-life of plutonium-240 is 6560 years.
The amount left after