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

Answer:

Dosage= 500 mg

Frequency= twice a day (every 12 hours)

Duration= 10 days

Number of dosage= 10*2= 20

residual drug amount after each dosage= 4.5%

We can build an equation to calculate residual drug amount:

• d= 500*(4.5/100)*t= 22.5t, where d- is residual drug, t is number of dosage

• After first dose residual drug amount is: d= 500*0.045= 22.5 mg

• After second dose: d= 22.5*2= 45 mg

As per the equation, the higher the t, the greater the residual drug amount in the body.

Maximum drug will be in the body:

• d= 20*22.5= 450 mg at the end of 10 days

Maximum drug will be in the body right after the last dose, when the amount will be:

• 500+19*22.5= 927.5 mg