Question

3) When a drug is administered to a patient, the amount A (in milligrams) of the drug in the patient's bloodstream t minutes after injection is approximated by A(t) = 175 - 175e-0.26 At what rate is the amount of the drug in the patient's bloodstream changing after 10 minutes?

Answer 1

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And Alt) = 1 - Alt) - 175 - 175 é ..2x It is amount of drugs in bloodstream. Now we know that derivative of ce function represents rate of change in function. So rate of change in the amount of drug in bloodstream will be given by Al(t). Now A' (t) = d (ALA)]

=) A (A) = d [175-175ė- 0.2t] - o - 175d (6-o. 2d) dt = -175 (-0.2) € 0.2 a leat) = a cat -) A (A) = 350-0.24 - 0

It is rate of change in amount after et minute. Now for rote of change after so minutes put t=10 in. A'llo) = 35€ 0:2 (10) A (10) = 35 & 2 = 35 Al10)= 4.73673491

So amount of drug in the batients bloodstream is changing at the rate 4.73673491 milligrams. per minute atfer 10 minute So answer is (4.7367349)) 4.7367 (after [ 73 67 rounding rounding