Calculus 1000A/B Lecture Notes - Exponential Growth, Exponential Decay, Morphine

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CALC 1000A/B Full Course Notes
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CALC 1000A/B Full Course Notes
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1. (a) the half-life of morphine in the bloodstream is 3 hours. Let f (t) be the amount of morphine in milligrams in the bloodstream at time t where t is in hours. Since the morphine undergoes exponential decay and there is initially 0. 4 mg in the system we have that f (t) = 0. 4ekt. 3 hours we have that 0. 2 = f (3) = 0. 4e3k and from this we get that k = Thus, we have that f (t) = 0. 4e ln ( 1. 3: to nd the amount of time it takes for there to be only 0. 01 mg left, we solve. 2) (cid:1) ln(cid:0) 1 ln(cid:0) 1 ln(cid:0) 1. 40 t t (cid:1) (cid:1) t = 3. After 1 minute there are 3 grams remaining and after 3 minutes there is only 1 gram remaining. Find x0 and the amount of kool-aid powder remaining after 5 minutes.

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