A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 76°C, it is cooling at a rate of 1°C per minute. Let y = T - Tg, where T(t) is the temperature of the coffee in degrees Celsius at time t and T, is the temperature of the surroundings in degrees Celsius. Find the values of A (in °C) and k for y(t) = Aekt A = 76 k = -1/53 X °C x After how many minutes is the temperature of the coffee 76°C? (Round your answer to two decimal places.) 0.34 X min

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 76°C, it is cooling at a rate of 1°C per minute.
Let y = T - Tg, where T(t) is the temperature of the coffee in degrees Celsius at time t and T, is the temperature of the surroundings in degrees Celsius. Find the values of A (in °C) and k for
y(t) = Aekt
A = 76
k = -1/53
X °C
X
After how many minutes is the temperature of the coffee 76°C? (Round your answer to two decimal places.)
0.34
X min
Transcribed Image Text:A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 76°C, it is cooling at a rate of 1°C per minute. Let y = T - Tg, where T(t) is the temperature of the coffee in degrees Celsius at time t and T, is the temperature of the surroundings in degrees Celsius. Find the values of A (in °C) and k for y(t) = Aekt A = 76 k = -1/53 X °C X After how many minutes is the temperature of the coffee 76°C? (Round your answer to two decimal places.) 0.34 X min
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