Answer:
The medication in the patient’s blood stream after 15 hours will be 5mg
Step-by-step explanation:
we can use formula
[tex]P(t)=P_0(\frac{1}{2} )^{\frac{t}{h} }[/tex]
P(t) is the amount of dose after t hours
t is the time in hours
Po is the initial amount of dose
h s the half life time
we are given
a medication has a half-life of 5 hours in a patient’s blood stream
[tex]h=5[/tex]
an initial dose of 40.0 mg is administered
so, we have
[tex]P_0=40[/tex]
now, we can plug these values
[tex]P(t)=40(\frac{1}{2} )^{\frac{t}{5} }[/tex]
now, we can plug t=15
[tex]P(15)=40(\frac{1}{2} )^{\frac{15}{5} }[/tex]
[tex]P(15)=40\cdot \frac{1}{2^3}[/tex]
[tex]P(15)=5[/tex]
So, the medication in the patient’s blood stream after 15 hours will be 5mg
