Answer:
[tex]t=46.13days[/tex]
Explanation:
Hello there!
In this case, since the radioactive decay is considered as first-order kinetic model, whereby the remaining mass of the radioactive material involves the initial one, the rate constant and elapsed time:
[tex]A=Ao*exp(-kt)[/tex]
As we were not initially given the rate constant, we can use the half-life to calculate it as follows:
[tex]k=\frac{ln(2)}{8.040days}=0.08621days^{-1}[/tex]
Thus, we can calculated the elapsed time for the given conditions to obtain:
[tex]t=\frac{ln(0.75g/40.0g)}{-0.08621days^{-1} }\\\\t=46.13days[/tex]
Regards!
