The University of Sydney
School of Mathematics and Statistics
Assignment 1
MATH1013: Mathenmatical Modelling Semester 2, 2021
Web Page: http://sydney.edu.au/science/maths/u/UG/JM/MATH1013/
Lecturers: Behrouz Taji and Pantea Pooladvand
This individual assignment is due by 11:59pm Thursday 26 August 2021, via
Canvas. Late assignments will receive a penalty of 5% per day until the closing
date. A single PDF copy of your answers must be uploaded in Canvas at https:
//canvas.sydney.edu.au/courses/34966. It should include your SID, your tutorial
time and day. Please make sure you review your submission carefully. What you see is
exactly how the marker will see your assignment. Submissions can be overwritten until
the due date. To ensure compliance with our anonymous marking obligations, please
do not under any circumstances include your name in any area of your assignment;
only your SID should be present. The School of Mathematics and Statistics encourages
some collaboration between students when working on problems, but students must
write up and submit their own version of the solutions. If you have technical difficulties
with your submission, see the University of Sydney Canvas Guide, available from the
Help section of Canvas.
This assignment is worth 2.5% of your final assessment for this course. Your answers should be
well written, neat, thoughtful, mathematically concise, and a pleasure to read. Please cite any
resources used and show all working. Present your arguments clearly using words of explanation
and diagrams where relevant. After all, mathematics is about communicating your ideas. This
is a worthwhile skill which takes time and effort to master. The marker will give you feedback
and allocate an overall letter grade and mark to your assignment using the following criteria:
Mark Grade Criterion
5 A Outstanding and scholarly work, answering all parts correctly, with clear
accurate explanations and all relevant diagrams and working. There are
at most only minor or trivial errors or omissions.
4 B Very good work, making excellent progress, but with one or two substantial
errors, misunderstandings or omissions throughout the assignment.
3 C Good work, making good progress, but making more than two distinct sub-
stantial errors, misunderstandings or omissions throughout the assignment.
2 D A reasonable attempt, but making more than three distinct substantial
errors, misunderstandings or omissions throughout the assignment.
1 E Some attempt, with limited progress made.
0 F No credit awarded.
Copyright c© 2021 The University of Sydney 1
This assignment contains only one question.
1. Let D(t) represent the amount of drug in a patient’s blood (measured in grams) at time
t (measured in hour). Assuming that the amount of drug decays exponentially, address
the following problems.
(a) Write down the differential equation that best describes the decay of the amount
of the drug.
(b) Find the general solution to the differential equation in part (a).
(c) After 2 hours the remaining amount of drug is 70 grams. Use this additional
information to uniquely determine D(t).
(d) What is the half-life for D(t) that you have found in (c)?
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