Title: “Exploring Functions and Designing a T-Shirt Logo for Mr A’s World Record Achievement”

Guidance for students
Using an appropriate set of axes, identify and record a number of data points on the curves which will allow you to develop model functions for them. 
Define all variables used and state any parameters clearly. 
Using technology, plot sets of data points on a graph. What type of functions model the behaviour of the data? 
Explain why you chose these functions. 
Find functions that represent the curves forming the logo. 
Discuss any limitations. 
The Mathematics department wishes to print a T-shirt using the design in Figure 1 on the back as a gift for Mr A to celebrate his world record marking assessment speed. 
Ms B must double the dimensions of the logo for this purpose. Describe how your functions must be modified.
What fraction of the area of the T-shirt design in Figure 1 does the Pi symbol occupy? 
Write a mathematical exploration that explains the process and addresses the questions above. 
Potential extensions to drive exploration forward:
You might want to consider how your work can be extended. This could mean extending the sophistication of the solutions you have already given to the points above, or exploring further points of interest regarding Mr A’s logo.
An example of an extension:
Ms B wants to stitch the pi logo to the T-shirt and she would like to calculate how much thread is needed.