#$&*
course Mth163
6/3 4
Here are some data for the temperature of a hot potato vs. time:Time (minutes)
Temperature (Celsius)
0
95
10
75
20
60
30
49
40
41
50
35
60
30
70
26
Graph these data below, using an appropriate scale:
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.
Using (10,75) (20,60) (60,30)
75 = a 10^2 + b 10 + c
60 = a 20^2 + b 20 + c
30 = a 60^2 + b 60 + c
Eliminate c from your equations to obtain two equations in a and b.
300a + 10b = -15
3200a + 40b = -30
Solve for a and b.
a = .015
b = -1.95
Write the resulting model for temperature vs. time.
temperature = .015(t^2) + -1.95(t) + 93
Make a table for this function:
Time (minutes)
Model Function's Prediction of Temperature
0, 93
10, 75
20, 60
30, 48
40, 39
50, 33
60, 30
70, 30
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 2
10 75 0
20 60 0
30 49 1
40 41 2
50 35 2
60 30 0
70 26 -4
Find the average of the deviations.
0.375
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).
The data observed was on point and fairly consistant to the formula.
Carefully read and understand the outlines and summaries of the modeling process as given below, as it applies to the examples discussed so far. Be sure to note the outline to be memorized (see the end of the page or click on the link To Be Memorized).
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
@&
Very good.
Note that you aren't asked to submit these exercises in this form. The Query at the end of the assignment will ask you questions about your work.
You are still welcome to submit work in this format. For questions that appear in the Query this might be redundant (no problem on this end, but consider the time it takes you to transcribe your work). For questions that don't appear in the Query, and on which you want feedback, this is the format to use.
*@