The strength of a radioactive substance decreases 50% in a 30-day period. How long will it take for the radioactivity to decrease to 1% of its initial value?
The standard formula for radioactive decay, as you know, is $\displaystyle N(t)=N_02^{-t/h}$, where $\displaystyle N_0$ is the initial amount, $\displaystyle t$ is the time elapsed, and $\displaystyle h$ is the half-life (with $\displaystyle h$ and $\displaystyle t$ being measured in consistent units). So for the material to reach 1% of its initial value, $\displaystyle \frac{N}{N_0}=.01$. Therefore, simply isolate t in the following equation: $\displaystyle .01=2^{-t/30}$