Question

Suppose that a medication has a half-life of 5 hours in a patient’s blood stream. If an initial dose of 40.0 mg is administered, how much of the medication will be in the patient’s blood stream after 15 hours? Show work or explain your reasoning.

Answer 1

Answer:

The medication in the patient’s blood stream after 15 hours will be 5mg

Step-by-step explanation:

we can use formula

$P(t)=P_0(\frac{1}{2} )^{\frac{t}{h} }$

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

$h=5$

an initial dose of 40.0 mg is administered

so, we have

$P_0=40$

now, we can plug these values

$P(t)=40(\frac{1}{2} )^{\frac{t}{5} }$

now, we can plug t=15

$P(15)=40(\frac{1}{2} )^{\frac{15}{5} }$

$P(15)=40\cdot \frac{1}{2^3}$

$P(15)=5$

So, the medication in the patient’s blood stream after 15 hours will be 5mg