Question 1208076: The concentration C of a medication in the bloodstream t hours after being administered is modeled by the function
C(t) = -0.002t^4 + 0.039t^3 - 0.285t^2 + 0.766t + 0.085
A. After how may hours will the concentration be highest?
B. A woman nursing a child must wait until the concentration is below 0.5 before she can feed him. After taking the medication, how long must she wait before feeding her child?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part A
I'll use x in place of t.
Type y = -0.002x^4+0.039x^3-0.285x^2+0.766x+0.085 into Desmos.
Here is the link
https://www.desmos.com/calculator
Notice if you clicked on the curve, a few points show up.
Click on the highest point to display the coordinates (2.1603, 0.75936)
Both of those decimal values are approximate.
Therefore, the max concentration is around 0.75936 which happens at the timestamp of roughly 2.1603 hours.
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Part B
Revisit the Desmos page where you typed in y = -0.002x^4+0.039x^3-0.285x^2+0.766x+0.085
In the box below that, type in y = 0.5
A horizontal line will show up.
This line intersects the curve in two locations.
Click the points of intersection to have their coordinates show up.
You should see (0.71326, 0.5) and (4.46534, 0.5)
The 0.5's are exact but the other decimal values are approximate.
When 0 < x < 0.71326, the concentration of the medication is between 0 and 0.5
This is the first window of opportunity the woman has to feed her child.
If she must wait for the concentration to go past 0.5 and then come down again, then this window must be ignored.
When 0.71326 < x < 4.46534, the concentration is above 0.5
After the 4.46534 hour marker (approximate), the concentration will dip below 0.5
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