*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 = *e*^{λt}* – 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 K**é**yah 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.