Keyah Math Module 12, Level 4
Mathematical Content: Exponential and logarithmic functions, algebraic operations, graphs
Finding the Age of the Earth: Level 4
Solution to Question 1.
Use the basic decay equation P(t) = P0e- λ t. When
t = half-life for Rb-Sr = 4.88 x 104 million years,
then the initial number of atoms is reduced by half (from 
to 
) , so denoting half-life by h, set t = h and solve 
for l.
,
So now we solve 
for λ, with h = 4.88 x 104.
Cancel P0 from each side, then take the natural logarithm of both sides,
But
so
.
We have found the decay constant λ = 1.42 x10-5 for the Rb-Sr system.
This material is based upon work supported by the National Science Foundation under Grant GEO-0355224. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.