Lab: Wetons Low of Cooling
When you drink something very hot, you have probably noticed that it quickly cools to a temperature that you consider tolerable. The drink then stays in a dinkable temperature range for quite a while. Newton's law of cooling provides us with a theoretical model for this situation. It states that the temperature difference betweenn the hot object and its surroundings decreases exponentially with time. We will use a temperature probe to collect data, which simulates variations that occur as a liuid cools.
The first thing that we did in this lab was finding the room temperature. This temperature was 72.9 degrees.
Second we got a cup of hot water for the experient. We placed the emperature probe in the cup for one minute. We then removed the probe from the water and used our calculator to see the graph of the temperature. Our data showed that the temperature values decreased and then eventually levelled off.
We then sketched a plot of our temperature against the time data in the window of our calculator.
The equation that we were using for this lab was Y = A (B) ^ X
Our horizontal asymptote was 0 which represented 72.9, the room temperature.
We then had to moify the equation above to include the asymptote. This resulted in Y = A (B) ^X + C
A: Initial Amount
B: Growth/decay Factor
C: Horizontal Asymptote at Room Temperature
X: Time in Seconds
Y: Temperature
As the time increases, the temperature starts to decrease.
We started plugging in the information that we knew into the equation. It now turned into Y = A (B) ^X + 72.9
We found the y-value when x was equal to zero. This point was (0, 142.5)
42.5 = A (B) ^0 + 72.9
=69.6 = A (B) ^ 0
A = 69.6
We now modified the equation again. Y = 69.6 (B) ^ 112 + 72.9
Now we had to use a send point from our data, which was: (112, 95.674)
95.674 = 69.6 (B) ^ 112= 79.9
= 22.774= 69.6 (B) ^ 112
(B ^112) ^ 1/112 =(.3372) ^ 1/112
B = .990075
The equation now turns from Y = A (B) ^ X + C to 5.674 = 69.6 (.990074) + 72.9
The first thing that we did in this lab was finding the room temperature. This temperature was 72.9 degrees.
Second we got a cup of hot water for the experient. We placed the emperature probe in the cup for one minute. We then removed the probe from the water and used our calculator to see the graph of the temperature. Our data showed that the temperature values decreased and then eventually levelled off.
We then sketched a plot of our temperature against the time data in the window of our calculator.
The equation that we were using for this lab was Y = A (B) ^ X
Our horizontal asymptote was 0 which represented 72.9, the room temperature.
We then had to moify the equation above to include the asymptote. This resulted in Y = A (B) ^X + C
A: Initial Amount
B: Growth/decay Factor
C: Horizontal Asymptote at Room Temperature
X: Time in Seconds
Y: Temperature
As the time increases, the temperature starts to decrease.
We started plugging in the information that we knew into the equation. It now turned into Y = A (B) ^X + 72.9
We found the y-value when x was equal to zero. This point was (0, 142.5)
42.5 = A (B) ^0 + 72.9
=69.6 = A (B) ^ 0
A = 69.6
We now modified the equation again. Y = 69.6 (B) ^ 112 + 72.9
Now we had to use a send point from our data, which was: (112, 95.674)
95.674 = 69.6 (B) ^ 112= 79.9
= 22.774= 69.6 (B) ^ 112
(B ^112) ^ 1/112 =(.3372) ^ 1/112
B = .990075
The equation now turns from Y = A (B) ^ X + C to 5.674 = 69.6 (.990074) + 72.9
Question:
J.H. Poincare (1854-1912), (cited in H.E. Huntley, The Divine Proportion, Dover, 1970)
"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful."
What is your reaction to this quote? What is your reaction when Cathy exclaims, "Math is beautiful!"
"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful."
What is your reaction to this quote? What is your reaction when Cathy exclaims, "Math is beautiful!"
Reaction:
This man must really like math. He enjoys spending time with it and has fun doing it.
When Cathy exclaims, "Math is beautiful!" I think she is some what crazy. I struggle with math and have a hard time enjoying it. When I do
When Cathy exclaims, "Math is beautiful!" I think she is some what crazy. I struggle with math and have a hard time enjoying it. When I do