*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) = P_{0}e- λ t. When

t = half-life for Rb-Sr = 4.88 x 10^{4} 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 10^{4}.

Cancel P_{0} 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.