The formula for solving this problem is exponential decay.:
R(t) = a (b)-t
Where:
b >1
1-b is the fraction of the amount of Radium taken out every year,
a = 300 is the starting life or size of Radium-226,
R(t) is the amount of Radium-226 after t years.
The half life of Radium-226 is 1590 years can be represented in an equation this way:
a/2 = a (b)-1590
divided by a on both sides:
1/2 = (b)-1590
(1/2)-1/1590 = [(b)-1590]-1/1590
b ≈ 1.0004360366594...
Therefore our function R(t) = 300(1.0004360366594...)-t
when t=2000
R(2000) = 3000(1.0004360366594...)-2000
R(2000) ≈ 125.45 mg.
