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)= 5/6(12t-t^2)
a) Determine the average rate of change of the amount of medicine ingested from
i. 4 to 6 hours ii. 6 to 8 hours
Compare the two rates with respect to the given situation
b) Estimate the slope of the tangent at the point p(4,80/3). Use an interval of 0.01. Round the final answer to the nearest hundredth. Explain what the values represents for this situation.
Math Help!?!?
2015-07-22 7:09 pm
回答 (1)
2015-07-22 7:52 pm
a) (A(6) - A(4))/2 = (30 - 80/3)/2 = 10/9 ≈ 1.11 ... mg/h for the period 4-6 hours.
.. (A(8) - A(6))/2 = (80/3 - 30)/2 = -10/9 ≈ -1.11 ... mg/h for the period 6-8 hours.
The amount ingested peaks out at 6 hours. The amount of medicine ingested is increasing up until that time, after which it is decreasing.
b) (A(4.005) - A(3.995))/.01 (26.6833 - 26.65)/.01 = 3.33 ... mg/h
This is the rate at which the medicine is being ingested at t=4 hours.
A(4) = 80/3 ≈ 26.67 ... mg. is the amount that has been ingested at t=4 hours.
.. (A(8) - A(6))/2 = (80/3 - 30)/2 = -10/9 ≈ -1.11 ... mg/h for the period 6-8 hours.
The amount ingested peaks out at 6 hours. The amount of medicine ingested is increasing up until that time, after which it is decreasing.
b) (A(4.005) - A(3.995))/.01 (26.6833 - 26.65)/.01 = 3.33 ... mg/h
This is the rate at which the medicine is being ingested at t=4 hours.
A(4) = 80/3 ≈ 26.67 ... mg. is the amount that has been ingested at t=4 hours.
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