Soon after taking an aspirin a patient has absorbed 280 mill

Soon after taking an aspirin, a patient has absorbed 280 milligrams of the drug. After 3 hours, only 35 milligrams remain in the bloodstream. Find an exponential model for the amount of aspirin in the bloodstream after t hours. HINT [See Example 2. f(t) = Use your model to find the amount of aspirin in the bloodstream after 4 hours. f(t) = milligrams

Solution

initial amount of drug = 280 milligrams

after 3 hours it is 35 milligrams

P = Po e^kt

35 = 280 e^(3t)

finding k

35/280 = e^3k

ln ( 35/280) / 3 = k

k = -0.69315

hence, model is

f(t) = 280 e^-0.69315 t

amount of aspirin after 4 hours

f(t) = 280 e^-0.69315 (4)

f(t) = 17.5 milligrams