Question 1208076
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Part A


I'll use x in place of t.
Type <font color=blue>y = -0.002x^4+0.039x^3-0.285x^2+0.766x+0.085</font> 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 <font color=blue>y = -0.002x^4+0.039x^3-0.285x^2+0.766x+0.085</font>


In the box below that, type in <font color=blue>y = 0.5</font>
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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