Applied Medicine Dosage

The exponential function function Decay and Geometric series in cargon for Dosage Abstract The problem facing by physicians is the event that for most doses thither is a minimum dosage beneath 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 minginess in the body of a patient. The exponential function dilapidate and geometric series and its formula are the powerful numeral tools for analysis of dose concentration. These two mathematical tools were used to harbinger the dose concentration of a drug in blood of a patient also, it empennage be maintained the train of drug dose. Exponential Growth A measure offer Q is said to be subject to exponential growth, Q(t), if the bill Q increases at a rate proportional to its cling to over condemnation t. Symbolically, this can be expressed as follows: dQ(t)dt That is, dQ(t)dt = kQ(t), w hich is a derivative equating. Where dQ(t)dt is the rate of change of quantity Q over age t, Q(t) is the reward of the quantity Q at age t, and k is a dictatorial 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 crosss around Q, because Q give 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 arbitrar y positive constant. Exponential Decay A q! uantity 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 privation to get a full essay, order it on our website: OrderEssay.net

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