Question

Sophia has an ear infection. The doctor prescribes a course of antibiotics. Sophia is told to take 500 mg doses of the antibiotic regularly every 12 hours for 10 days. Sophia is curious and wants to know how much of the drug will be in her body over the course of the 10 days. She does some research online and finds out that at the end of 12 hours, about 4.5% of the drug is still in the body.
A. What quantity of the drug is in the body right after the first dose, the second dose, the third dose, the fourth dose?


B. When will the total amount of the antibiotic in Sophia’s body be the highest? What is that amount?


C. Answer Sophia’s original question: Describe how much of the drug will be in her body at various points over the course of the 10 days?

Answer 1

Step-by-step explanation:

A) The amount is taken during the first dose is - 500 mg

In 10 days, she will take the drugs for 240/12 = 20 times

After 12 hours, 4.5 % of drugs remain in the blood therefore

after the first dose = 500

second dose, 4.5% of  500 + 500 = 22.5 +500 = 522.5 mg

third dose, 4.5 % of 522. 5 + 500 = 523.51 mg

Forth dose, 4. 5% of 523.51 + 500 = 523.55 mg

B) Highest amount will be found on 20th dose.

= 500 x (1-0.045^20/ 1- 0.045)

= 523.55 mg

C) The highest amount in the body is near to 523.55 mg therefore after 10 days also, the amount of drug will remain near the value of 523.55 mg.