Keyah Math Module 8, Level 2
Mathematical Content : Exponential and logarithmic functions, algebraic operations, graphs
Age of the Earth: Solution
Solve the equation
0.0205 = eλt – 1,
with λ = decay constant for Rb-Sr = 1.42 x10-5, for t.
We present two solutions, one is algebraic, the other is graphic using the plot-solve applet.
Algebraic solution.
Solve 
Take the natural logarithm of both sides and then solve for t,
.
The gabbro is, approximately, 1,429 million years old.
Graphical solution.
To solve the equation 
, graph each side and determine the point of intersection.
(The graph shown below is copied from the Earth Math or Kéyah Math website Plot/Solve applet.)
The gabbro is, approximately, 1,429 million years old.
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.