First, we have the next data:
Q(t) = final mass at time t = 10 g
Qo = initial mass = 40 g
v = decay constan = 0.00043 1/years
This kind of process like decay, follow a first-order reaction, and the formula used for this:
[tex]\begin{gathered} Q(t)=Qoxe^{-vxt} \\ \text{Clearing t:} \\ \frac{Q(t)}{Qo}=e^{-vxt} \\ \ln (\frac{Q(t)}{Qo})=-\text{vxt} \\ \frac{\ln (\frac{Q(t)}{Qo})}{-\text{v}}=t \end{gathered}[/tex][tex]\begin{gathered} \frac{\ln (\frac{10}{40})}{-0.00043\text{ 1/years}}=\text{ t} \\ \end{gathered}[/tex]
Answer: t = 3224 years
