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course Mth 173
9/23 1:29 PM
The Celsius temperature of a hot potato placed in a room is given by the function T = 40* 2- .007 t + 24 , where t is clock time in seconds and T is temperature in Celsius. At what average rate is the temperature of the potato changing between clock times t = 6.8 and t = 6.9 seconds seconds?
T = 40 * 2 - .007 (6.8) + 24 = 55.9524
T = 40 * 2 - .007 (6.9) + 24 = 55.9517
55.8517 - 55.9524 = -.0007
6.9 - 6.8 = .1
- .0007 / .1 = -0.007 celsius/s avg rate of temperature change.
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You have calculated the average rate of change to only one significant figure.
Your calculation is correct, but the number of significant figures is insufficient for this problem.
You will need to calculate this quantity to a number of significant figures sufficient to make comparisons between the average rates, as calculated for different time intervals.
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At what average rate is the temperature of the potato changing between clock times t = 6.8 and t = 6.81 seconds?
T = 40 * 2 - .007 (6.81) + 24 = 55.95233
55.95233 - 55.9524 = -.00007
-.00007 / .01 = -0.007
At what average rate is the temperature of the potato changing between clock times t = 6.8 and t = 6.801 seconds?
T = 40 * 2 - .007 (6.801) + 24 = 55.952393
-.000007 / .001 = -0.007
What do you estimate is the rate at which temperature is changing at clock time t = 6.8 seconds?
-0.007
The rate at which the Celsius temperature of a hot potato placed in a room is given by Rate = .041 * 2- .007 t, where R is rate of change in Celsius degrees per second and t is clock time in seconds.
How much temperature change do you estimate would occur between t = 6.8 and t = 13.6 seconds?
r = .041 * 2 - .007 t
.041 * 2 - .007 (6.8) = 0.0344
.041 * 2 - .007 (13.6) = -0.0132
-0.0476 / 2 = -0.0238
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You didn't indicate where the -.0476 came from, though I can see what you did. However you need to show where every number comes from. The basic idea is 'no mystery numbers'.
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13.6 - 6.8 = 6.8
-0.0238 * 6.8 = -0.16184 temperature change.
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You've calculated half the change in the rate, the multiplied it by the time interval in order to get the change in temperature.
This doesn't make sense. For example, if the rate stayed constant (and nonzero) there would be 0 change in the rate, and half that would be 0, so you would conclude that the temperature didn't change.
The definition of rate:
The average rate of change of A with respect to B is (change in A) / (change in B).
The A quantity here is temperature, the B quantity is clock time, and you are trying to find the change in temperature.
How therefore should you proceed?
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You did the right calculations on the first problem but didn't have enough significant figures to compare your results. It should be easy to revise that one.
On the second problem you did not correctly apply the definition of rate of change. That one might take a little more thought.
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