Question

Soon after taking an aspirin, a patient has absorbed 280 mg of the drug. After 2 hours, only 70 mg remain. 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)= ____mg.

Answer 1

Y = 300e^(-Bt) 
plug in y = 75 and t = 2 
75 = 300e^(-2B) 
75/300 = e^(-2B) 
ln(75/300) = -2B 
B = -ln(75/300) / 2 
so B = approx 0.693300 = A(e^0) = A 
A = 300 
. 9.4 mg left in the bloodstream after 5 hours.