See my note and see if you can supply a little more information so I can be sure you got a reasonable model.
I'm not for sure if I calculated the temps using the models correctly. I used the formula T=(TO-Tr)2^-(kt)+Tr. I just don't think there should be that big of a difference between the calculated and the observed." "?Determine the time required for the smaller (faster) probe to approach halfway from its initial temperature to the 75 degree Fahrenheit room temperature? I determined that it would take 1-?minutes.
?Determine the time required to then approach halfway to room temperature from this temperature? I determined it would take 2.5 minutes.
?Determine the time required for the next halfway approach? I determined it would take 4 minutes.
?Determine the time required to approach halfway to room temperature starting at 20 degrees Fahrenheit? I determined it to be 2 minutes.
?Average the halfway times to estimate the half-life of this probe? I determined the half-life to be 2.5 minutes.
?Determine the time required for the larger (slower) probe to approach 25% of the way from its initial temperature to room temperature? I determined it to be 3.5 minutes.
?Determine the time required to approach 25% of the way to room temperature from that point? I determined it to be 4 minutes.
?Determine also the time required to approach halfway to room temperature from the initial temperature? 9 minutes.
?Why is this time not equal to the sum of the two 25% approach times? It is not equal because the probe began to increase as a faster rate as time increased.
?Using either model of the temperature, determine the temperature of the smaller probe as predicted by the function for each of your observed clock times. Compare with observed temperatures and report how close the model is to the observations.
Smaller Probe
Time Observed Temperature Calculated Temperature
1 ?min 38.3 50.78
4 min 57.2 69.13
8 min 66.4 74.06
Larger Probe
Time Observed Temp. Calculated Temp.
1 ?min 8.8 16.2
4 min 20.9 35.2
8 min 35.1 53.5
You need to show your specific model. You say which function you used but you don't connect that function to your data or show how you got (T0 - Tr) or k.
?At what temperature are the temperatures of the two probes most different. 57.2 Degrees
?At what temperature do the two probes appear to be changing at the same rate? 52.6 degrees.
?Find the temperature at which the model predicts the greatest temperature difference. At temp at 1 ?min.