Re: The Cooling Law Problem
Okay, you have to determine two values, a and b, so you need two equations. Typically, it is best two use two distant points on the graph, here, x= 0, y= 98 and x= 5, y= 68.
Originally Posted by nabey1
That is, solve and [itex]68= ab^5[/itex] for a and b. Once you have found a and b, determine .
Is this your answer? It's not clear to me what you are saying. Why does "the suggested one" have limited predictive power? Why are the other models you show not helpful?
b) What is worrying about this prediction?
This raises a worrying aspect of fitting regression models to data. An exponential relationship seems plausible, and yet the suggested one has limited predictive power. Indeed other regression models fit the data well, but are not helpful as predictors for the situation (see below).
c) Develop a model by creating a new list of 'excess' temperatures (T - 18.5), and again doing the standard exponential regression on (T - 18.5) versus t. What temperature does this predict after 30 mins? How does this compare with the model from part a)
d) From an analysis of your answers in part a), b) and c), justify when it would be best to add the milk to the cup of black coffee to give the best chance of a nice hot cup of coffee if the phone rings : before answering the phone or after the brief phone call has ended.