Hey everyone, do you think you can 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

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