Problem Solving (80 marks) Answer all questions using and applying what you have learnt in this course. Unless otherwise specified, full verbal and mathematical explanations of your answers are required.

· Graphs (figures or diagrams) must be clearly and correctly labelled.

· Graphs are required to be drawn by hand (either on paper or in a tablet), or generated using Desmos or GeoGebra. If generated with Desmos or GeoGebra you have to explain, and where suitable show the derivation of the expressions you used to create the graphs. Graphs generated with any other software/applications will not be marked.

· Unless otherwise specified, use y on the vertical axis and x on the horizontal axis.

· All prices and quantities are to be treated as continuous and non-negative variables.

· Round numerical calculations to two decimal places where appropriate. Unless otherwise specified, all variables can take any real value (not necessarily only discrete values).

Use of AI. This task has been designed to be challenging, authentic and complex. Whilst students may use artificial intelligence (AI) and/or machine translation (MT) technologies, successful completion of assessment in this course will require students to critically engage in specific contexts and tasks for which artificial intelligence will provide only limited support and guidance. Marks are awarded for your reasoning, clarity, and demonstration of course knowledge.

Indicate in which parts of this examination AI or MT was used to answer the questions. For instance, “AI was used in parts 1(a), 2(b), and 3(a).” Acknowledgement of use of AI or MT will not result in lower marks, but failing to do this may constitute student misconduct under the Student Code of Conduct.

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