Applications of Calculus - Mathematical Modelling - Mathematics Assignment Help

Assignment Task :

Purpose:

To provide evidence of your learning in relation to the following assessment design criteria:

• Concepts and Techniques

• Reasoning and Communication

Medical Researcher Tess Tubes spends her days collecting data from a multitude of studies and trying to fit mathematical models to accurately represent the various scenarios. In doing so, her focus is not simply on finding a function that is the best possible fit to a set of data points, but rather on finding a function that is a reasonable fit and whose properties provide insight into the situation being modelled. In aspiring to join her team, you have been given some of her cases to work on so that you can demonstrate your mathematical prowess and prove your worth.

Firstly, in a study investigating Blood Alcohol Concentration (BAC), a group of males were asked to rapidly consume two drinks. Their BAC was recorded over time (in minutes since the beginning of the drinking period) and the average BACs calculated. In the table below, a value of B(t) = 27 at a particular time means that the average of the values of each participant’s Blood Alcohol

Tess has suggested that a possible mathematical model for this data is in the following surge function: Bt=2.66te-0.023t. Your task here is to display the data and the function on a graph and report back on the suitability of this model. Your comments should include discussion of the properties of this curve that make it an appropriate model, areas of inaccuracy and any limitations.

In a second study, data has been collected on the rate of change of nicotine concentration in the blood over time. In the data set shown below, the rate, C’(t) is measured in milligrams of nicotine per decilitre of blood per hour and time t is measured in hours since smoking one cigarette.

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