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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 respect 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.
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