Here I am, stuck at home with a bad ear infection. I have to take 250 mg of ampi

Question

Here I am, stuck at home with a bad ear infection. I have to take 250 mg of ampicillin four times a day (that is, every 6 hours). No fun! I feel like it will last forever. And that made me think, how much ampicillin would I have in my body if I really did take 250 mg every 6 hours forever? I can't think clearly right now, but can you figure it out? The pharmacist says it will level off eventually, because even though I'm taking more and more, it's eliminated from the body over time. Specifically, after 6 hours, 4% of the dose is still in the body. Will that mean it levels off though? It won't add up to infinity? Maybe you could list how much (in milligrams) is in the body immediately after I take the first tablet (okay, that's 250 mg), immediately after the second tablet (okay, that would be 4% of the first dose plus another 250 mg), immediately after the third tablet (ummm, 4% of the 4% of the first dose, plus 4% of the second dose, plus the full third dose, but my brain is getting tired now), and immediately after the fourth tablet? That would be the first day. Is there a formula or some way to write down the pattern? And what will it all add up to? Infinity? Or a specific amount of ampicillin? Of course you'll show me how you get the answers so the next time I have to take any medicine I can just find out how quickly that particular medicine is eliminated from the body and I'll be able to calculate the long-run level of it in my body! Thanks!

Explanation / Answer

S=250+250*4%+250*4%*4%+250*4%4%4%+250*4%4%4%4%+-------- uto infinity

S= 250 ( 1+ 4% + 4%.4%+4%.4%.4%+ 4%.4%.4%.4%+--------- upto infinity )

the term in bracket is in GP with a=1 and r = 4%

we know the sum to infinty in GP = a/(1-r)

thus

S= 250 * 1/(1-4%) = 250/(1-0.04) =250/0.96=260.4167

thus at very long time total amount of drug in body is 260.4167 gm

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.