The function A(t) = 200e^-0.014t gives the amount of medication, in milligrams, in a patient's bloodstream t minutes after the medication has been injected into the patient's bloodstream.

Question

(a) Find the amount of medication, to the nearest milligram, in the patient's bloodstream after 40 minutes.
? mg

(b) Use a graphing utility to determine how long it will take, to the nearest minute, for the amount of medication in the patient's bloodstream to reach 50 milligrams.
? min

Answer 1

a)
plug 40 into t in the original equation

b)
solve for t analytically
t = 99.021

heres a graph:
http://www.wolframalpha.com/input/?i=200e%5E%28-.014t%29%3D50