SOLUTION: S. Bones is the doctor in Deathly, Ill., a suburb of Chicago. One day, John Garfinkle comes in with a high fever. Dr. Bones takes a blood sample and finds that it contains 1300 flu

Question 59515: S. Bones is the doctor in Deathly, Ill., a suburb of Chicago. One day, John Garfinkle comes in with a high fever. Dr. Bones takes a blood sample and finds that it contains 1300 flu viruses per cubic millimeter and is increasing. John immediately gets a shot pf penicillin. The virus count should continue to increase for a while, then (hopefully!) level off and go back down. After 5 minutes the virus count is up to 1875, and after 5 more minutes, it is 2400. Assume the virus count varies quadratically with the number of minutes since the shot.
Find the equation expressing the number of viruses per cubic millimeter in terms of the number of minutes since the shot. Be sure to define your variables, set up a system of equations and use matrices to solve. Show all steps.
Answer by hayek(51) (Show Source):
You can put this solution on YOUR website!
t=0: 1300 flu/cc
t=+5min: 1875 flu/cc
t=+10min: 2400 flu/cc
The problem tells us "the virus count varies quadratically with the number of minutes since the shot", so it is in this form:
.
Let's plug in the data we have in order to solve for a, b and c:
Eq.1:
Eq.2:
Eq.3:
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Eq. 1 ==>
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Plug that result into Eq.2:
, then solve for a:

Eq. 4:
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Now, plug that result into Eq.3:

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Using that result in Eq. 4, we have:

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So the formula for virus count in terms of time in minutes is:
.
You can plug in the data to check that the formula is correct.
Here is a graph: