[Math] Radioactive Decay formula is $A=A_0e^{-kt}$. How many years until 10 grams decay so that only 8 remain

Question

I have been trying this question for hours and come to a dead end every time…

Consider the radioactive decay formula $A=A_0e^{-kt}$ where $A$ is the amount of radium remaining at the time $t$. $A_0$ is the amount present initially and $k$ is the decay constant. After how many years would 10 grams of radium decay so that only 8 grams remain. (The half-life of radium is 1,590 years)

Answer 1

First you need to figure out $k$.

Suppose $t$ is in years, then you know that ${1 \over 2 } = e^{-1590k}$. Use this to compute $k$.

Now you need to figure out $t$ such that $8 = 10 e^{kt}$.