Question

Soon after taking an aspirin, a patient has absorbed 280 mg of the drug. After 3 hours, only 35 mg remain. Find an exponential model for the amount of aspirin in the bloodstream after t hours.

Answer 1

Let A be the amount of aspirin in milligrams at time t.
When t = 0, A = 280 mg. ------ (a)
When t = 3 hours, A = 35 mg. ------ (b)

\(\Large \frac{35}{280} = \frac{5}{40} = \frac 18\)

Therefore, \(\Large A = 280\left( \frac 18\right )^{t/3} \) ----- (1)

Put t = 0 in (1), we get A = 280 mg. (satisfies (a))
Put t = 3 in (1), we get A = 280 * 1/8 = 35 mg. (satisfies (b))