Answer:
55.5556 hours.
Explanation:
Let's solve the problem.
The amount of dopamine rate applied to a person is based on the formula: 10mcg/kg/min. Such relation can be express as follows:
(10mcg/kg/min)=
(10mcg/kg)*(1/min)
Now by multiplying by the weight (12 kg) of the 2 years old person, we have:
(10mcg/kg)*(1/min)*(12kg)=
(10mcg*12kg/kg)*(1/min)=
(120mcg)*(1/min)=
120mcg/min, which is the rate of dopamine infusion, which can be express as:
(120mcg/min)*(60min/1hour)=
(120mcg*60min)/(1hour*1min)=
7200mcg/hour=
1hour/7200mcg, which means that for each hour, 7200mcg dopamine are infused.
Because the D5W product has 400 mg of dopamine, then we need to convert 400 mg to X mcg of dopamine in order to use the previous obtained rate. This means:
Because 1mcg=0.001mg then:
(400mg)*(1mcg/0.001mg)=
(400mg*1mcg)/(0.001mg)=
400000mcg, which is the amount of dopamine in D5W.
Now, using the amount of dopamine in D5W and the applied rate we have:
(rate)*(total amount of dopamine)=hours of infusion
(1hour/7200mcg)*(400000mcg)=hours of infusion
(1hour*400000mcg)/(7200mcg)=hours of infusion
(55.5556 hours) =hours of infusion
In conclusion, the infusion will last 55.5556 hours.