Question

# A child with an ear infection is given a 200-mg ampicillin tablet once every four hours....

1. A child with an ear infection is given a 200-mg ampicillin tablet once every four hours. About 12% of the drug in the body at the start of a four-hour period is still there at the end of that period. Calculate the quantity of ampicillin in the body right after taking the third tablet is given. If we keep on giving tablets to the child forever, what level of the drug in the body do we converge to? Explain.

If the child is given medicine after every 4 hours of 200 mg dose.

12% of 200 mg dose is there after 4 hours.

Thus drug level in the body after 4 hours = 200 * (0.12)^1 = 24 mg

Thus when child takes second medicine after 4 hours, the dose would become 224 mg(200 + 24). Thus 12% of dose after 8 hours = 26.88 mg

Thus when child takes third medicine after 8 hours, the dose would become 226.88 mg(200 + 26.88).

If we keep on giving medicine to child the dose 24 + (24 * 1.12) + (24 * 1.12 * 1.12) + (24 * 1.12 * 1.12 * 1.12) and so on.....

Thus According to sum of GP series of infinite terms.

a = 24, r = 1.12

Sum = a / (r-1)

Sum = 200

Thus extra dosage apart from the medicine dose would converge to 200 if you keep on giving medicines to child.