Question

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.

Answer 1

we can use y = Ae^(-Bt) where y represents the amount of aspirin in the bloodstream, t is time, and 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 we can solve for 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

so there is approx. 9.4 mg left in the bloodstream after 5 hours.

Hope this helps.

Answer 2

Thank you so much! Makes better sense now!

Answer 3

you could also use just the numbers given
\[\large A(t)=280\times \left(\frac{35}{280}\right)^{\frac{t}{3}}\]

Answer 4

But if the time would be 3, what would "a" be?

Answer 5

I am still trying to figure where the 300 came from. From what is given in the first part allows you to compute the constant A as shown but I don't "remember" y=300 ???

Answer 6

Wasn't y=280, thats what I remember.