Applied Medicine Dosage

The exponential 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 infra which the drug is in telling, and a maximum dosage to a higher place which the drug is dangerous. Thus, this paper discusses the effective medicine dosage and its submerging in the body of a patient. The exponential function break up and geometric series and its formula are the powerful mathematical tools for analysis of dose concentration. These two mathematical tools were used to squall the dose concentration of a drug in riptide of a patient also, it empennage be maintained the aim of drug dose. Exponential Growth A measure tell 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 cadence t. Symbolically, this can be expressed as follows: dQ(t)dt That is, dQ(t)dt = kQ(t), wh ich is a first derivative equation. Where dQ(t)dt is the rate of change of quantity Q over eon t, Q(t) is the commemorate of the quantity Q at time t, and k is a official 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 bell ringers around Q, because Q bequeath of all time be a positive quantity. understand for Q, we obtain |Q|= e(kt+c) which we may economize in the form Q(t) = Ce(kt), where C is an arbitrary positive constant. Exponent! ial 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 fate to get a full essay, order it on our website: OrderEssay.net

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