A doctor injects you with 500 milligrams of a radioactive compound for medical imaging. It has a half-life of 6 hours. How long will it take for 99.9% of it to decay? Round to the nearest hour.
Answer
99.9*500 = 500e^kt
99.9 = e^kt
99.9 = e^6k
ln99.9 = lne^6k
4.6041 = 6k
k = 0.76736
I actually made some progress. Now I'm stuck here. How do i proceed?
Always divide percentages by $100$ to get proportions in contexts like this. If $99.9\%$ (a proportion of $0.999$) has decayed, you're left with $0.001$ times the original total. Let's work in hours. Since $e^{-6k}=\frac12$, $e^{-kt}=0.001\implies t=6\frac{\ln 1000}{\ln 2}\approx60$.