I have a simple question. Let's say that we have A amount of a substance that has a half life of 100 years, calculate the rate of decay per annum. I was able to do this question with e but I showed my solution to my teacher and he said there was an easier way of doing it. Any help is appreciated.
Previous Solution:
$\lim_{x\to\infty}(1-\frac{r}{x})^x = e^{-r}$
$e^{-r} = 0.5$.
therefore $r = -\ln(0.5)$ (rate per 100 years).
$r_2\; \mathrm{(rate\ per\ year)} = \frac{r}{100} = 0.7\%$
