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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
a)

A=500e%5E%28-0.165t%29 Start with the given equation.


A=500e%5E%28-0.165%2A5%29 Plug in t=5


A=500e%5E%28-0.825%29 Multiply -0.165 and 5 to get -0.825


A=500%280.43823499246482%29 Evaluate e%5E%28-0.825%29 to approximately get 0.43823499246482


A=219.11749623241 Multiply


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


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b)

A=500e%5E%28-0.165t%29 Start with the given equation.


100=500e%5E%28-0.165t%29 Plug in A=100


100%2F500=e%5E%28-0.165t%29 Divide both sides by 500.


0.2=e%5E%28-0.165t%29 Divide


ln%280.2%29=ln%28e%5E%28-0.165t%29%29 Take the natural log of both sides.


ln%280.2%29=-0.165t%2Aln%28e%29 Pull down the exponent.


ln%280.2%29=-0.165t%2A1 Evaluate the natural log of 'e' to get 1.


ln%280.2%29=-0.165t Multiply.


%28ln%280.2%29%29%2F%28-0.165%29=t Divide both sides by -0.165 to isolate 't'.


9.75416916626728=t Evaluate the left side with a calculator.


So the solution is approximately t=9.754 (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