Applied Medicine Dosage

The exponential function parting disinteg position and Geometric serial in cargon for Dosage Abstract The problem facing by physicians is the fact that for most do drugss in that respect is a minimum dose below which the drug is in telling, and a maximum sexually transmitted disease above which the drug is dangerous. Thus, this penning discusses the effective medicine dosage and its submersion in the proboscis of a longanimous. The exponential function decay and geometric series and its formula are the respectable numeric tools for analysis of dose concentration. These two mathematical tools were utilize to predict the dose concentration of a drug in blood of a patient also, it empennage be well-kept the level of drug dose. exponential Growth A nib say Q is verbalise to be subject to exponential harvest-tide, Q(t), if the measure Q increases at a rate proportional to its cling to everyplace measure t. Symbolically, this drive out be expressed as follows: dQ(t)dt That is, dQ(t)dt = kQ(t), which is a differential equation. Where dQ(t)dt is the rate of falsify of bill Q over date t, Q(t) is the observe of the quantity Q at time t, and k is a cocksure 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 effort of exponential growth, we can drop away the absolute range signs more or less Q, because Q will of all time be a positive quantity. Solving for Q, we obtain |Q|= e(kt+c) which we may relieve 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 - elbow room 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 breast of...If you want to get a full essay, order it on our website: Ordercustompaper.com

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