 
Summary: A RADIOACTIVE DECAY CHAIN
MATH2573H, SPRING 2012, UNIVERSITY OF MINNESOTA
GREG W. ANDERSON
Here is an example which motivates our study of systems of differential equations.
Setup
Suppose that we have three radioactive elements, namely conium, cubium and
spherium, with halflives of 2.7, 4 and 8 months, respectively. [Oops I said 2 months
in class but I should have said 2.7 to make the following numbers work out.] It then
works out that (approximately, to keep the numbers simple) the decay constants
for these elements are 3
·
= ln 2
(2.7/12) , 2
·
= ln 2
4/12 , and 1
·
= ln 2
8/12 , respectively, e.g., one
pound of cubium decays after t years to e2t
