Applied Medicine Dosage

The exponential function function Decay and Geometric series in cargon for Dosage Abstract The problem facing by physicians is the item that for most doses thither is a minimum dosage to a lower place which the drug is in telling, and a maximum dosage higher up which the drug is dangerous. Thus, this paper discusses the effective medicine dosage and its concentration in the body of a patient. The exponential function moulder and geometric series and its formula are the powerful mathematical tools for analysis of dose concentration. These two mathematical tools were used to foretell the dose concentration of a drug in pedigree of a patient also, it empennage be maintained the take of drug dose. Exponential Growth A measure give voice Q is said to be subject to exponential growth, Q(t), if the measure Q increases at a rate proportional to its cling to over cartridge holder t. Symbolically, this can be expressed as follows: dQ(t)dt That is, dQ(t)dt = kQ(t), which is a differential equivalence. Where dQ(t)dt is the rate of change of quantity Q over clip t, Q(t) is the disclose of the quantity Q at clock t, and k is a verifying 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 exit of all time be a positive quantity. solution 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)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 penury to get a full essay, order it on our website: OrderEssay.net

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