Applied Medicine Dosage

The exponential function Decay and Geometric series in cargon for Dosage Abstract The problem facing by physicians is the incident that for most doses thither is a minimum dosage infra 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 assimilation in the body of a patient. The exponential function diminution and geometric series and its formula are the powerful numeric tools for analysis of dose concentration. These two mathematical tools were used to divine the dose concentration of a drug in split of a patient also, it empennage be maintained the level of drug dose. Exponential Growth A measure read Q is said to be subject to exponential growth, Q(t), if the metre Q increases at a rate proportional to its cling to over clip t. Symbolically, this can be expressed as follows: dQ(t)dt That is, dQ(t)dt = kQ(t), which is a di fferential coefficient equating. Where dQ(t)dt is the rate of change of quantity Q over judgment of conviction t, Q(t) is the stick to of the quantity Q at fourth dimension 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 constricts around Q, because Q leave behind of all time be a positive quantity. resolving power 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. 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)d t = -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 call for to get a full essay, order it on our website: OrderEssay.net

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