Respuesta :
We have been given that the half life of radium is 1690. And the present amount is 50 grams.
It means that after 1690 hours the amount remain will be 25 grams.
The exponential formula is given by
[tex]A=Pe^{rt}\\\\25= 50 e^{r\cdot 1690}\\\\\frac{1}{2}=e^{r\cdot 1690}\\\\\\\text{Take natural log both sides}\\\\\ln(\frac{1}{2})=\ln(e^{r\cdot 1690})\\\\\ln(\frac{1}{2})=1690r\\\\r=\frac{1}{1690} \times \ln(\frac{1}{2}\\\\r=-0.00041[/tex]
Now, we have to find A for t = 760 years
[tex]A= 50e^{-0.00041 \cdot 760}\\\\A=36.61 \text{ grams}[/tex]
