Originally Posted by

**drewbear** $\displaystyle

(\frac{1}{2})^\frac{x}{20}

$

you use the 1/2 as your base because its a half life, and then it is to the x power, but since the half life only occurs every 20 years the x is over 20.

Now to find when there is less than 90% of the chemical you simply set the equation equal to .1, aka 10%, and solve.

$\displaystyle

(\frac{1}{2})^\frac{x}{20}=0.1

$

$\displaystyle

\log_\frac{1}{2} 0.1=\frac{x}{20}

$

$\displaystyle

\frac{\log 0.1}{\log \frac{1}{2}}=\frac{x}{20}

$

$\displaystyle

x=20(\frac{\log 0.1}{\log \frac{1}{2}})

$

$\displaystyle

x=66.439ish

$