Drug question calculus?
A person enters a hospital for 24 hours and is given a drug. If t is in hours since the drug was administered, the concentration, in ng/ml, of a drug in the persons bloodstream is given by
The person is told complications can occur if they leave the facility and the concentration is above 4 ng/ml. Should the patient worry?
- Steve4PhysicsLv 74 weeks ago
No calculus is needed. All we need to do is find the concentration when t=24 hours and see if it less than 4ng/ml.
C(24) = 55 * 24 * e^(-0.25*24) = 3.27 ng/ml
So it is safe for the patient to leave aftewr 24 hours.
- 4 weeks ago
4 = 55 * t * e^(-t/4)
4/55 = t * e^(-t/4)
t = 0.074
t = 23.0316
In either case, t < 24. All we need to do now is find C(24)
55 * 24 * e^(-24/4) =>
110 * 12 * e^(-6) =>
1320 / e^6 =>
So we know that they're going to be fine. We know that the only time the drug was ever at a dangerous concentration or higher was when they were at the facility and the drug is well below the dangerous threshold when they leave.