# Math Help - Radioactive Decay

1. ## Radioactive Decay

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?

2. The standard formula for radioactive decay, as you know, is $N(t)=N_02^{-t/h}$, where $N_0$ is the initial amount, $t$ is the time elapsed, and $h$ is the half-life (with $h$ and $t$ being measured in consistent units). So for the material to reach 1% of its initial value, $\frac{N}{N_0}=.01$. Therefore, simply isolate t in the following equation: $.01=2^{-t/30}$