contestada

Diana is sick in hospital with a severe bacterial infection. she is to be fed antibiotics intravenously at a constant infusion rate, and the doctor knows that the anti-biotic will be eliminated from the bloodstream at a rate proportional to the amount y(t) present in the bloodstream at time t. if the half-life of the anti-biotic in the bloodstream is 3 hours, what rate of infusion should he prescribe to maintain a long-term amount of 400 mgs in diana's bloodstream? 1. infusion rate = 1.694 mgs/min 2. infusion rate = 1.617 mgs/min 3. infusion rate = 1.848 mgs/min 4. infusion rate = 1.771 mgs/min 5. infusion rate = 1.54 mgs/min

Respuesta :

Infusion rate=1.167mgs/mins3
oladayoademosu

The answer is 5. infusion rate 1.54 mgs/min

Since the amount in the blood stream at any time, t is y(t), and

Since the anti-biotic will be eliminated from the bloodstream at a rate proportional to the amount y(t) present in the bloodstream at time t, we have that

-dy(t)/dt ∝ y(t)

-dy(t)/dt = ky(t) where k = proportionality constant = rate constant

Now, k = 0.693/t where t = half-life of antibiotic = 3 hours = 3 × 60 min = 180 min.

Since the rate at which the antibiotic is eliminated from the blood equals the infusion rate and we require an amount of y(t) = 400 mgs, the infusion rate is

dy(t)/dt = ky(t)

dy(t)/dt = 0.693 × 400/180

dy(t)/dt = 277.2/180

dy(t)/dt = 1.54 mgs/min

So, the infusion rate is 1.54 mgs/min

So, the answer is 5. infusion rate 1.54 mgs/min

Learn more about infusion rate here:

https://brainly.com/question/11451592

Otras preguntas