Applied Medicine Dosage

The exponential function Decay and Geometric series in cargon for Dosage Abstract The problem facing by physicians is the fact that for most doses thither is a minimum dosage beneath which the drug is in telling, and a maximum dosage preceding(prenominal) which the drug is dangerous. Thus, this paper discusses the effective medicine dosage and its immersion in the body of a patient. The exponential function tumble and geometric series and its formula are the powerful numeric tools for analysis of dose concentration. These two mathematical tools were used to prognosticate the dose concentration of a drug in furrow of a patient also, it empennage be maintained the take of drug dose. Exponential Growth A measure aver Q is said to be subject to exponential growth, Q(t), if the measuring stick Q increases at a rate proportional to its cling to over sequence t. Symbolically, this can be expressed as follows: dQ(t)dt That is, dQ(t)dt = kQ(t), w hich is a first derivative equality. Where dQ(t)dt is the rate of change of quantity Q over prison term t, Q(t) is the witness of the quantity Q at conviction t, and k is a affirmative number called the growth constant.

Now, we can clobber for the differential equation dQ(t)dt= kQ(t) Separating the variables and integrating, we have ?dQ(t)dt = ?kdt so that ln |Q|= kt +C In the case of exponential growth, we can drop the absolute value compresss around Q, because Q give of all time be a positive quantity. resolution for Q, we obtain |Q|= e(kt+c) which we may economize in the form Q(t) = Ce(kt), w here C is an arbitrary positive constant. E! xponential Decay A quantity Q is said to be subject to exponential decay, Q(t), if the quantity Q decreases at a rate proportional to its value over time t. This can be expressed as follows: That is, dQ(t)dt = -kQ(t) where the negative sign - means the decrease in the quantity Q over time t. By solving this differential equation, we obtain Q(t) = q?e(-kt) Where q?is the heart of...If you indispensability to get a full essay, order it on our website: OrderEssay.net

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