Stage 1 Mathematical Methods Assessment Type 2: Mathematical Investigation Rates of Cooling In this task you will develop formulae to model the relationship between the number of degrees of a cup of coffee and the time in minutes that have passed since the coffee was poured. The room temperature was measured as 20°C. a Section 1 Using Desmos or GeoGebra, plot the graph of A against t. Describe the general trend of the data. Using Desmos or GeoGebra, fit a linear model (y=mx+c) and an exponential model (y=k×a^x+b) to the data. Provide the algebraic formula for each model and interpret the values of the models in context. Discuss the reasonableness of each model, including their limitations and justify the most appropriate model for the data provided. Use your algebraic model to predict the temperature of the coffee after 2.5 minutes, 13 minutes, 35 minutes and 60 minutes after the coffee is poured. Predict how long it might take for the coffee to reach 5°C above room temperature. Confirm this prediction using algebraic methods. Discuss which prediction(s) would be the most and least accurate, consider the reasonableness and limitations of these predictions. Section 2 Consider what other factors might affect the rate of cooling of the coffee. Choose one factor to investigate and predict how you expect it might affect the temperature of the coffee over time. Design an experiment where two variations of your chosen factor are used and all other parameters are kept consistent. Through direct measurement produce a table similar to the table above for each of these two new situations. Graph your data and fit appropriate algebraic models. Analyse your data, graphs and models to draw a logical conclusion to your investigation. Compare your findings to your original prediction. Include a discussion of the reasonableness of your conclusions and any limitations to your investigation. The investigation report should be a maximum of 8 single-sided A4 pages if written.