Applied Medicine Dosage

The exponential function function Decay and Geometric series in cargon for Dosage Abstract The problem facing by physicians is the occurrence that for most doses thither is a minimum dosage under which the drug is in telling, and a maximum dosage in a higher place which the drug is dangerous. Thus, this paper discusses the effective medicine dosage and its compactness in the body of a patient. The exponential function disintegration and geometric series and its formula are the powerful numeric tools for analysis of dose concentration. These two mathematical tools were used to bespeak the dose concentration of a drug in stock certificate of a patient also, it empennage be maintained the train of drug dose. Exponential Growth A measure theorize Q is said to be subject to exponential growth, Q(t), if the measuring rod Q increases at a rate proportional to its cling to over quantify t. Symbolically, this can be expressed as follows: dQ(t)dt Th at is, dQ(t)dt = kQ(t), which is a differential coefficient equating. Where dQ(t)dt is the rate of change of quantity Q over eon t, Q(t) is the keep on of the quantity Q at metre t, and k is a optimistic 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 preindications around Q, because Q testament of all time be a positive quantity. declaration for Q, we obtain |Q|= e(kt+c) which we may eco! nomize in the form Q(t) = Ce(kt), where C is an arbitrary positive constant. Exponential 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 take to get a full essay, order it on our website: BestEssayCheap.com

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