StudentShare
Search

# Modelling the Amount of a Drug in the Bloodstream - Assignment Example

Summary
"Modelling the Amount of a Drug in the Bloodstream" paper models the amount of drug (μg) for the treatment of malaria in the bloodstream. The model function that represents the amount of drug over the period is derived and the suitability of this model function is discussed. …

## Extract of sample "Modelling the Amount of a Drug in the Bloodstream"

Download file to see previous pages The amount of drug (μg) for treatment of malaria in the bloodstream after an interval of 0.5 hours (30 minutes) for 10 hours is recorded in the given graph as shown in figure 1. From this graph, the values of the amount of drug (μg) after 0.5 hours are taken and presented in table 1. Below figure 2 is plotted based on table 1 data.

However, it is easier for modeling when we take the value of ‘n’ as ‘e’1 because for simplifying exponential equation it is easier to take the value of ‘n’ as ‘e’. this type of exponential equation is called as “natural exponential equation”2 and can be written as :

The above equation is a natural exponential equation of growth, i.e. the value of will increases as the value of x increases. If we replace ‘c’ to ‘-c’, then this equation will become a natural exponential equation of decay.

Now, from figure 2 graph it is obvious that the amount of drug decreases with time, therefore it is of type of an exponential decay graph. A natural exponential decay function can be represented by:3

From the above figure 3, it is seen that the graph of model function follows a similar decrease (decay) as the data given for the amount of drug remained over a period of time. Therefore, the model function represents the type of decay that is given in a graph of figure 1.

The patient is instructed to take 10 µg of a drug every six-hour. From a given graph (figure 1 and table 1), it is seen that the amount of drug remained after six hours is 3.7 µg. Let assume that this is the amount of decrease for every six-hour period. Therefore, when the second dose is given to the patient than the initial amount will be 13.7 µg at the start of the 7th hour. Similarly, at the start of the 13th, and 19th hour the initial amount will be 17.4 µg and 21.1 µg respectively. This is presented in below table 3.

The patient is instructed to take 10 µg of the drug every six-hour.  ...Download file to see next pagesRead More
Cite this document
• APA
• MLA
• CHICAGO
(Modelling the Amount of a Drug in the Bloodstream Assignment, n.d.)
Modelling the Amount of a Drug in the Bloodstream Assignment. https://studentshare.org/mathematics/1710545-mathematics
(Modelling the Amount of a Drug in the Bloodstream Assignment)
Modelling the Amount of a Drug in the Bloodstream Assignment. https://studentshare.org/mathematics/1710545-mathematics.
“Modelling the Amount of a Drug in the Bloodstream Assignment”. https://studentshare.org/mathematics/1710545-mathematics.
Click to create a comment or rate a document

## CHECK THESE SAMPLES OF Modelling the Amount of a Drug in the Bloodstream

### Bloodstream Infections

..., cardiovascular devices, urinary catheter and penile implants .Other causes blood infections includes use of unscreened blood products, and contact between patients. For central line associated bloodstream infections, they are actually associated with increased length of hospitalization (Guerin, 2010). In USA, it has been reported that increased risk of developing blood stream infections (BSI) is associated with the increased use of central venous catheters (CVSs) in ICU patients especially when the skin catheter site is colonized by bacteria and fungi. This is a major risk factor for CVC infection. Other predisposing factors to infection includes; exposure to mechanical ventilations (Jerome, 2000). Patients receiving TPN are also at risk...
7 Pages(1750 words)Research Paper

### Central line associated bloodstream infections

...? Central Line Associated Bloodstream Infections Central Line Associated Bloodstream Infections Central line-associated bloodstream infections (CLABSIs) cause thousands of deaths annually and billions dollars of costs to the United States healthcare system, although these infections can be prevented. Central line-associated bloodstream infections (CLABSIs) happen when microbes get into the bloodstream by a central line (a tube that is inserted in a large vein to provide blood, medications, fluids, or to do specific medical tests rapidly. The long duration of hospitalization before catheterization, underlying medical circumstances, prematurity, area of placement of catheter or various other factors may result in increased risks of central...
3 Pages(750 words)Research Paper

### Mathematical Modelling

...? Mathematical Modeling al Affiliation) Introduction The paper applies the second-order differential equations in variousreal life situations. Most of the questions involve the masses that bounce up and down at the spring’s end. The questions apply the accurate descriptions of the motion under various motions of situations. The work also introduces a lot of results and notions that are equally applicable in things that oscillate and vibrate in similar manner. For instance, the current analysis in fundamental circuit is analogous to analysis involving the spring’s mass. Discussion Diagram representing the (MSD) System Source: "Mass-Spring-Damper." File:Mass-Spring-Damper (2 body system).svg. N.p., n.d. Web. 28 Nov. 2013.
4 Pages(1000 words)Math Problem

### Modelling (Spreadsheet Modelling for OR)

From the above chart it is clear that there has been an increase in population among the age 20 to 25 than any other age group, this is a positive indication of the population because this shows an increase in the regions workforce.
The above chart shows that there has been a population increase among the young females, however there has been a decline in population among those aged above 40 years, this is evident from our above chart which shows higher death rates among the old yet a very low levels of population aged between 40 years and above.
The total rate from our data shows that the death rate total amounts to 1181.5 while that of the birth rate amounts to 871, when we proceed and find the mean rates then our mean...
3 Pages(750 words)Essay

### Bussiness modelling

In the same manner the information system being developed should not be the automation of the current operational bad habits in the organization. Information System development should also include transforming the operation of the organization from being person or people centric to process and procedure centric as defined by its operating policies and business goals.
In information system development before starting the actual design of the system, we need to analyze and understand the requirement and the process of the organization and also the people that will be affected by the system. The system can either contribute to the organization’s success or it could also be the reason for the demise of an organization in case of i...
4 Pages(1000 words)Essay

### Financial modelling

...FINANCIAL MODELING By of the of the School Briefly explain the conceptsof expected return, standard deviation, and correlation (in the context of share prices), and discuss their importance in portfolio management. The fundamental concept behind Modern Portfolio Theory (MPT) is the fact assets in an investment portfolio should generally not be selected individually, each and every one on its own merits. It is very necessary to consider how each and every asset changes in price relative to how every other asset in the portfolio changes in price. The process of investment is basically a tradeoff between expected return and risk. Generally, it is thought that assets with much higher expected returns are more risky. For any given amount...
6 Pages(1500 words)Lab Report

...Business Modelling By Key words: Principles, Simulation Introduction Business modeling has been used for so long to solve business problems and develop strategies for the success of these businesses. There are so many models that can be used for this purpose. This paper will look at some of these models and their strengths and limitations. Linear Regression Analysis Strengths This is a technique of statistical analysis that helps business managers, economists and even business researchers forecast on the trends of their businesses in the coming future. Regression analysis will give the trends of the variables and this relationship will give a clear picture on what to expect in the future (Curwin, Slater and Eadson 2013). It also helps...
8 Pages(2000 words)Essay

### Financial Modelling

...FINANCIAL MODELLING Introduction In this report, we attempt to explore whether a company should introduce a profit sharing scheme for all employees. Two theoretical principles have been postulated before. One postulates that introduction of profit sharing scheme will improve employee satisfaction and organisational commitment. The other theory argues that there will be greater alignment of employee and employer interests if such a scheme is introduced. Six variables have been used to conduct a quantitative analysis. The variables are; Profit margin of company (expressed as a percentage), Total assets of company (expressed in £ millions), Extent of team working within the company (expressed as a percentage), Scheme (coded as 1 if company...
7 Pages(1750 words)Research Paper

### Mathematical modelling

...Mathematical Modelling al Affiliation Mathematical modelling is a fundamental way of using mathematics to solve real world situations. The solution involves both a theoretical approach to describe the system in general, and a mathematical approach where numerical answers are required. This report uses roller coaster and rectangular area problems to demonstrate the application of mathematical modelling using differentiation. Introduction Explaining mathematical modelling In as much as mathematical modelling is mathematics, it is also a theoretical science, thus offers mathematical answers to both narrow questions requiring numerical answers, and broach questions that require a description of general behaviour. In mathematics, modelling...
3 Pages(750 words)Essay

### Modelling the Amount of a Drug in the Bloodstream

...Math Portfolio- Modelling the Amount of a Drug in the Bloodstream Math Portfolio- Modelling the Amount of a Drug in the Bloodstream Introduction Thismathematics portfolio will model the amount of drug in the bloodstream based on the data given for a drug for treating malaria in the bloodstream over the 10-hour period following an initial dose of 10 μg. After modelling the amount of drug in bloodstream, a comparison will be made in-between graph of model function and graph of data given so that suitability of the model function can be determined (part A). After that in part B, various cases for malaria patient who is instructed to take 10 μg drug doses after every six hours will be taken. In addition, maximum and minimum drug dose for 24...
6 Pages(1500 words)Lab Report