Answer:
11 days.
Explanation:
According to the statement, the radioactive isotope has a half-life greater than 1 day and lesser than 7 days. Let assume that the radioactive isotope has a half-life of 4 days and the initial mass is 50 mg. The time constant is:
[tex]\tau = \frac{4\,days}{\ln 2}[/tex]
[tex]\tau = 5.771\,days[/tex]
The time when mass is reduced to 8 milligrams is:
[tex]t=-(5.771\,days)\cdot \ln\frac{8\,mg}{50\,mg}[/tex]
[tex]t \approx 10.576\,days[/tex]
It is approximately 11 days.
