course mth271
Pick three representative points and circle them.Write the equations that result from the assumption that the appropriate mathematical model is a quadratic function y = a t^2 + b t + c.
Temp.= 1/60(t^2)-2.083(t)+95
Eliminate c from your equations to obtain two equations in a and b.
Solve for a and b.
Write the resulting model for temperature vs. time.
Make a table for this function:
Time (minutes) Model Function's Prediction of Temperature
0 95
10 75.86
20 60.
30 47.51
40 38.35
50 32.52
60 30
70 30.86
Sketch a smooth curve representing this function on your graph.
Expand your table to include the original temperatures and the deviations of the model function for each time:
Time (minutes) Temperature (Celsius) Prediction of Model Deviation of Observed Temperature from Model
0 95 95 0
10 75 75.867 -.867
20 60 60 0
30 49 47.6 -1.4
40 41 38.35 -2.65
50 35 32.52 -2.48
60 30 30 0
70 26 30.86 4.86
Find the average of the deviations.
-.867-1.4-2.65-2.48+4.86/7 the total of the deviation divided by the number of enters gives us the average of -.362
Comment on how well the function model fits the data. (Note: the model might or might not do a good job of fitting the data. Some types of data can be fit very well by quadratic functions, while some cannot).
It seems to work in places but not at 100% the average deviation makes it look very good but being off by nearly 5 at T= 70 seems high
depending on what's being observed and how accurately it's being observed, deviations may be small or large
&#Good responses. Let me know if you have questions. &#