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. What quantity of the drug is in the body right after the first dose, the second dose, the third dose, the fourth dose (10 points)? When will the total amount of the antibiotic in Sophia’s body be the highest? What is that amount (10 points)? 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 (10 points).

Answer 1

At the end of first 12 hours = 22.5mg

At the end of the first day = 45mg

At the end of the tenth day = 450mg

Explanation:

Hello,

Sophia's doctor prescribed 500mg of drug for her every 12hrs.

At the end of 12 hours, she found out she has 4.5% of the drug in her blood.

What is the amount of the drug in her blood after 12 hours?

After 12 hours = 4.5 / 100 = x / 500mg

x = (4.5 × 500) / 100

x = 22.5mg

At the end of the first 12 hours, she has 22.5mg of the antibiotic in her body.

2. At the end of the second dose, she has

22.5mg + 22.5mg = 45mg of the drug in her body

3. at the end of the third dose, she has (22.5 + 22.5 + 22.5)mg in her body = 67.5mg

4. At the end of the fourth dose, she has (22.5 + 22.5 + 22.5 + 22.5)mg in her body = 90mg

Since 1 day contains 24hrs = 2 × 12hrs

The amount of drug present in her body at the end of the first day = (22.5 + 22.5)mg = 45mg

Assuming the concentration of the drug does not decrease over the course of the 10 days, there's an increase of 45mg of the antibiotic in her body every day

First day = 45mg

Second day = 45mg × 2 = 90mg

Third day = 45mg × 3 = 135mg

Fourth day = 45mg × 4 = 180mg

Fifth day = 45mg × 5 = 225mg

Sixth day = 45mg × 6 = 270mg

Seventh day = 45mg × 7 = 315mg

Eighth day = 45mg × 8 = 360mg

Ninth day = 45mg × 9 = 405mg

Tenth day = 45mg × 10 = 450mg

At the end of the tenth day, the amount of antibiotic present in her blood would be 450mg