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Question 936329: S. Bones is a doctor in Chicago, Illinois and one day sees a patient with a high fever. Dr.Bones takes A blood sample in fines that it contains 1300 flu viruses per cubic millimeter and is increasing. he immediately administers a shot of penicillin to the patient. now, the virus count should continue to go up for a while, then (hopefully!) level off and go back down. after five minutes, the virus count is up to 1875. after five more minutes it is 2400. Assume that the virus count varies quadratically with the number of minutes since the flu shot was given.
a)find the quadratic equation modeling this Virus count per cubic millimeter in terms of the number of minutes since the shot. this can be accomplished by setting up a three variable system and solving for a, b, and c.
b)Dr.Bones realizes that if the count ever reaches 4500, the patient must go to the hospital. will he need to go? explain using the discriminant.
c)according to your model, will the flu be completely cured?
d)what is the domain and range of the quadratic function?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Dr.Bones takes A blood sample in fines that it contains 1300 flu viruses per cubic millimeter and is increasing. he immediately administers a shot of penicillin to the patient. now, the virus count should continue to go up for a while, then (hopefully!) level off and go back down. after five minutes, the virus count is up to 1875. after five more minutes it is 2400. Assume that the virus count varies quadratically with the number of minutes since the flu shot was given.
a)find the quadratic equation modeling this Virus count per cubic millimeter in terms of the number of minutes since the shot. this can be accomplished by setting up a three variable system and solving for a, b, and c.
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Points:: (0,1300) ; (5,1875) ; (10,2400)
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ax^2 + bx + c = y
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Using (0,1300):: 0 + 0 + c = 1300
Using (5,1875):: 25a + 5b + c = 1875
Using(10,2400)::100a + 10b + c = 2400
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Using a matrix method get a = -1 ; b = 120 ; c = 1300
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Equation:: y = -x^2 + 120x + 1300
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b)Dr.Bones realizes that if the count ever reaches 4500, the patient must go to the hospital. will he need to go? explain using the discriminant.
Solve -x^2 + 120x + 1300 = 4500
-x^2 + 120x - 3200 = 0
Discriminant:: b^2 - 4ac = 120^2 - 4*-1*-3200 = 1600
Ans:: Since the quadratic has solutions the count might reach
4500 and the patient must go to the hospital.
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c)according to your model, will the flu be completely cured?
d)what is the domain and range of the quadratic function?
Domain:: 0<=x <= 130
Range:: 0<= y <= 4900
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Cheers,
Stan H.
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