Mr. Java pours a cup of hot coffee, then sets it aside and forgets about it. Ove

Question

Mr. Java pours a cup of hot coffee, then sets it aside and forgets about it. Over the next several minutes, the coffee cools down according to the equation at the left.

equation: y= 55(0.7)^t + 75

1. Find the ratio between y(1) and y(0)
2. Find the ratio between y(7) and y(6)
3. Ordinarily, these ratios would be equal to "b" (which is 0.7 in this problem) However, these ratios are different why?
4. Find y(15) and y(20). Why do you think these answers are so close together?

Fill in table:
Time Temp.
(min) (deg. f)
t y
0
1
2
3
4
5
6
7

Explanation / Answer

y(1)=113.5 y(0)=130 ratio= .873 y(7)=79.5 y(6)=81.47 ratio=.98 These ratios are different because of the factor of (+75). this will always remain ame and not increase in the same ratio. y(15)=75.26 y(20)=75.04 These 2 are so close because of the cooling function. Theoretically, it cools at this speed and it reaches very close to 75. Mathematically the more t increases, the temperature will reduce at a slower speed. 0-130 1-113.5 2-101.95 3-93.865 4-82.81 5-84.24 6-81.47 7-79.5

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