Application of Mathematics in Forensic Investigation

Summative Assignment Applications of Mathematics in Forensic Science
Assignment instructions
This assignment is summative for the module and accounts for 40% of the final mark.
Your completed work must be uploaded onto Tabula by Friday 8th December 2023 at 12 noon. Late submissions will incur a late penalty in line with standard University regulations.
Please ensure that your work has your student ID printed on it and not your name. This enables anonymity in the marking.
In this assignment you will investigate and study “Rate of cooling of a body to determine the approximate time of death” in a murder investigation.
Your report should be 1500 words long, but will also contain tables and figures. These will not contribute towards the word count.
Your report should be typed using Calibri font, size 12.
Any mathematical notation used must be inserted professionally using Microsoft Equation Editor or an equivalent tool.
In order to structure your report well and include relevant content you should complete the tasks listed and structure each task appropriately in the form of a report.
You will be marked on your ability to undertake mathematical calculations, interpret quantitative data and present information in a professional and informative way. Marks will also be awarded for accuracy of the information reported, creativity and for following the strict rules regarding layout as outlined above.
The assignment will be marked out of 100 and indicative marks per task are provided.
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Applications of Mathematics in Forensic Science
Rate of cooling of a body
The rate of cooling of a body can be used to determine the approximate time of death in a murder investigation. This assignment requires you to investigate the rate of cooling of a ‘body’ and formulate a model that can be used by investigators to estimate the time of death.
Format of report
Abstract (6 marks)
State purpose of investigation; brief method (graphs); brief theory; main results; model formulated.
Introduction
(i) Explain why estimation of the time of death is important in a murder investigation. (4 marks)
(ii) Briefly explain how rates of cooling can be used to determine the approximate time of death. (4 marks)
(i) Explain what’s cooling? (i.e. explain what causes a body to cool). (2 marks)
(ii) State and briefly explain the mechanisms of energy transfer. (4 marks)
(iii) Explain Newton’s law of cooling: include relevant equation. (4 marks)
(iv) Show that the solution of Newton’s law of cooling is an exponential function given by the
expression: θ = θ0e-kt
where θ = difference in temperature between the body and the surrounding, θ0 and k are constants to be determined. (6 marks)
You are provided with experimental data to investigate the rate of cooling of a body.
I. Use the data to verify Newton’s law of cooling and determine the cooling constant, k.
(i) Using excel, draw a graph of temperature against time (6 marks) and use your graph to determine the rates of cooling at four
different temperatures. (8 marks)
(ii) Enter your results in the table provided and determine the cooling constant. (4 marks)

II. Using excel, draw appropriate graphs to determine if the data can be represented by an exponential function. (12 marks)
Use your graphs to determine the values of θ0 and k. (6 marks)
Compare the cooling constant, k with the value obtained from part (I). (2 marks)
III. Discuss your results using appropriate scientific language.
Explain how the results of your investigation can be used by Forensic Scientists and the Police to estimate the time of death. (4 marks)
Conclusion and evaluation
(i) Discuss the main findings of the investigation. (4 marks)
(ii) Discuss the relevance/implication of your findings in a murder investigation. (2 marks)
(iii) Compare your results with literature. (4 marks)
(iv) Make an evaluation of the methods used/Discuss sources of error in your method used to
analyse the data. (4 marks)
(v) Make realistic suggestions how the investigation may be improved. (4 marks)
(vi) Suggest any further investigations that may be carried out. (2 marks)
References
Include the references you have used to write this report. (4 marks) Presentation (4 marks)
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Cooling investigation
Results: Summary
Surrounding (room) temperature, Ts = ————
Temperature, T °C
Cooling rate, R
(gradient)
(T – Ts) °C
Cooling constant
k = R/(T – Ts) min-1
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