As a pot of coffee cools down, the temperature of the coffee is modeled by a differentiable function C, for 0 sts 12, where time t is measured in minutes and the temperature C(t) is measured in degrees Celsius. Selected values of t are shown in the table. t (minutes) 35 78 12 C(t) (degrees Celsius) 64 55 48 43 41 36 (a) Evaluate C'(t) dt. Indicate units of measure. Explain the meaning of your answer in the context of the problem. The value of C'(t) dt represents the total temperature lost v from t = 0 to t = 12. (b) Explain the meaning of C(t) dt in the context of the problem. The value of C(t) dt represents the average temperature v from t = 0 to t = 12. Use a trapezoidal sum with 5 subintervals indicated by the table to approximate C(t) dt. Indicate units of measure. (Round your answer to one decimal place.) (c) Use the data in the table to approximate the rate, in °C per minute, at which the temperature is changing at time t = 6. (Round your answer to one decimal place.) °C per minute (d) For 12 st s 15, the rate of cooling is modeled by C'(t) = -2 cos(0.5t). Based on the model, what is the temperature of the coffee, in °C, when t = 15? Assume C(t) is continuous at t = 12. (Round your answer to two decimal places.) °C
As a pot of coffee cools down, the temperature of the coffee is modeled by a differentiable function C, for 0 sts 12, where time t is measured in minutes and the temperature C(t) is measured in degrees Celsius. Selected values of t are shown in the table. t (minutes) 35 78 12 C(t) (degrees Celsius) 64 55 48 43 41 36 (a) Evaluate C'(t) dt. Indicate units of measure. Explain the meaning of your answer in the context of the problem. The value of C'(t) dt represents the total temperature lost v from t = 0 to t = 12. (b) Explain the meaning of C(t) dt in the context of the problem. The value of C(t) dt represents the average temperature v from t = 0 to t = 12. Use a trapezoidal sum with 5 subintervals indicated by the table to approximate C(t) dt. Indicate units of measure. (Round your answer to one decimal place.) (c) Use the data in the table to approximate the rate, in °C per minute, at which the temperature is changing at time t = 6. (Round your answer to one decimal place.) °C per minute (d) For 12 st s 15, the rate of cooling is modeled by C'(t) = -2 cos(0.5t). Based on the model, what is the temperature of the coffee, in °C, when t = 15? Assume C(t) is continuous at t = 12. (Round your answer to two decimal places.) °C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:As a pot of coffee cools down, the temperature of the coffee is modeled by a differentiable function C, for 0 sts 12, where time t is measured in minutes and the temperature C(t) is measured in degrees Celsius. Selected values of t are
shown in the table.
t (minutes)
3
5
7
8
12
C(t) (degrees Celsius)
64
55
48
43
41
36
(a) Evaluate
C'(t) dt. Indicate units of measure.
Explain the meaning of your answer in the context of the problem.
The value of
C'(t) dt represents the total temperature lost
v from t = 0 to t = 12.
(b) Explain the meaning of
C(t) dt in the context of the problem.
The value of -
C(t) dt represents the average temperature
from t = 0 to t = 12.
Use a trapezoidal sum with 5 subintervals indicated by the table to approximate
C(t) dt. Indicate units of measure. (Round your answer to one decimal place.)
°C
(c) Use the data in the table to approximate the rate, in °C per minute, at which the temperature is changing at time t = 6. (Round your answer to one decimal place.)
°C per minute
(d) For 12 st < 15, the rate of cooling is modeled by C'(t) = -2 cos(0.5t). Based on the model, what is the temperature of the coffee, in °C, when t = 15? Assume C(t)
places.)
continuous at t = 12. (Round your answer to two decimal
°C
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