Question

Please Help Exponential Decay Word problem
suppose a person takes a fever reducer medicine that contains ibuprofen. After two hours, the amount of ibuprofen remained in the body is 120 mg and after 6 hours the amount reduced to 30 mg.
A. find an exponential decay function that models the amount of Ibuprofen in the body after t hours.

Answer 1

120mg 30mg
2h 6h

decreased by 1/4 in 4h

so \[\frac{1}{4} = 120e^{-k(4)} = [A]_{t} = [A]_{0}e^{-kt}\]

solve for -k

Answer 2

Ignore that 120 in the first part

you know that it took 4 hours to get to 30mg

so solve for k by \[\frac{1}{4} = e^{-k(4)}\]

e is the natural log