Answer:
The patient is allowed to leave after 12.02 hours from the time of ingestion of the medicine.
Explanation:
[tex]\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]
[tex]A=A_o\times e^{-\lambda t}[/tex]
Where:
[tex]\lambda [/tex]= decay constant
[tex]A_o[/tex] =concentration left after time t
[tex]t_{\frac{1}{2}}[/tex] = Half life of the sample
Half-life of  Technetium-99m =[tex]t_{\frac{1}{2}}[/tex]= 6.01 hours.
[tex]\lambda =\frac{0.693}{6.01 hour}=0.1153 (hour)^{-1}[/tex]
[tex]A_o=x[/tex]
75% of medic en must have been decayed before leaving the hospital. Then percentage of left over concentration of medicine will be: 100% - 75% = 25%
[tex]A=25\%of x=0.25x[/tex]
Time elapsed during this process= t
[tex]0.25x=x\times e^{-0.1153 (hour)^{-1}\times t}[/tex]
t = 12.02 hours
The patient is allowed to leave after 12.02 hours from the time of ingestion of the medicine.
