Hey everyone, do you think you can help me with this problem? 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.
What we can use is y = Ae^(-Bt) formula y = the amount of aspirin in the bloodstream t = time A and B are constants. start by solving for A by plugging in t = 0 and remembering that y = 300.
300 = A(e^0) = A
A = 300 next solve B as follows: 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 0.693 so our exponential model is y = 300(e^-.693t)
to find the amount in the bloodstream after 5 hours, we simply plug in t = 5 and we get: y = 300(e^(-.693*5)) = ~9.4 mg That is basically the ammount of miligrams in 5 hours
