Question 1042099: The amount of active ingredient of medicine ingested by the body, A in milligrams, is a function of time, t, in hours, given by A(t)=5/8(12t-t^2).
a)Determine the average rate of change of the amount of medicine ingested during each of the intervals below and compare the two rates with resect to the given situation.
4 to 6 hours and 6 to 8 hours.
b) Estimate the slope of the tangent at the point P(4,80/3). Use interval of 0.01. Round final answer to the nearest hundredth. Explain what the value represents for this situation.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The amount of active ingredient of medicine ingested by the body, A in milligrams, is a function of time, t, in hours, given by A(t)=5/8(12t-t^2).
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a)Determine the average rate of change of the amount of medicine ingested during each of the intervals below and compare the two rates with respect to the given situation.
4 to 6 hours and 6 to 8 hours.
A(4) = (5/8)(48-16) = 160/8
A(6) = (5/8)(72-36) = 180/8
A(8) = (5/8)(96-64) = 160/8
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rate from 4 to 6 hrs:: (180/8-160/8)/2 = 20/16 = 5/4 = 1.25 ml per hr
That means the rate at which the medicine is ingested is increasing.
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rate from 6 to 8 hrs:: (160/8-180/8)/2 = -1.25 ml per hr
That means the rate at which the medicine is ingested is decreasing.
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b) Estimate the slope of the tangent at the point P(4,80/3). Use interval of 0.01. Round final answer to the nearest hundredth. Explain what the value represents for this situation.
Note: (4,80/3) is not a point of the function; (4,20) is a point of the function.
Cheers,
Stan H.
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