SOLUTION: If 500 milligrams of anestesia are injected into a patient prior to surgery and the amout A in milligrams in the patient after t hours is given by the equation A=500e-0.165t the -0

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Question 376325: If 500 milligrams of anestesia are injected into a patient prior to surgery and the amout A in milligrams in the patient after t hours is given by the equation A=500e-0.165t the -0.165t is suppose to be up like a square on 500e but didn't know how to put it up there.
a) the amount of anestesia left after 5 hours.
b) when the amount of anesthesia remaining in the patient will be 100mg.
Can you help ! I'm suppose to do it on the calulator but can't figure it out.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
a)

Start with the given equation.


Plug in


Multiply -0.165 and 5 to get -0.825


Evaluate to approximately get


Multiply


So approximately 219.117 mg (rounded to the nearest thousandth) will be left after 5 hrs.


-----------------------------------------------

b)

Start with the given equation.


Plug in


Divide both sides by 500.


Divide


Take the natural log of both sides.


Pull down the exponent.


Evaluate the natural log of 'e' to get 1.


Multiply.


Divide both sides by -0.165 to isolate 't'.


Evaluate the left side with a calculator.


So the solution is approximately (rounded to the nearest thousandth)


So in about 9.754 hours, there will be 100 mg left over.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

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