Question

Use the following information. The antibiotic clarithromycin is eliminated from the body according to the formula A(t) = 500e−0.1386t, where A is the amount remaining in the body (in milligrams) t hours after the drug reaches peak concentration. How much time will pass before the amount of drug in the body is reduced to 100 milligrams? (Round your answer to two decimal places.)

Answer 1

The antibiotic clarithromycin is eliminated from the body according to the formula

$A(t) = 500e^{-0.1386t}$

where A is the amount remaining in the body (in milligrams) t hours after the drug reaches peak concentration

We need to find the time 't' when amount of drug is reduced to 100

Plug in 100 for A(t)  and solve for t

$100 = 500e^{-0.1386t}$

Divide both sides by 500

$\frac{1}{5} = e^{-0.1386t}$

Take ln on both sides

$ln(\frac{1}{5}) = ln(e^{-0.1386t})$

$ln(\frac{1}{5}) = -0.1386tln(e)$

$ln(\frac{1}{5}) = -0.1386t$

divide both sides by -0.1386

t = 11.6121

11.61 hours will pass before the amount of drug in the body is reduced to 100.