SOLUTION: The exponential 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 int

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Question 1130982: The exponential 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.
(a) Find the amount of medication, to the nearest milligram, in the patient's bloodstream after 35 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 by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The exponential function should be written as:
A%28t%29+=+200e%5E%28-0.014t%29
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.
(a) Find the amount of medication, to the nearest milligram, in the patient's bloodstream after 35 minutes._______mg
A%28t%29+=+200e%5E%28-0.014%2A35%29
A%28t%29+=+200e%5E%28-.49%29
A(t) = 200*.6126
A(t) = 122.5 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
Graph equation: y = 200*e^(-.014x)
+graph%28+300%2C+200%2C+-60%2C+170%2C+-100%2C+180%2C+200%2Ae%5E%28-.014x%29%2C+50%29+
Amt of 50 mg will occur at 99 minutes (green line is 50 mg)