7. For 0

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
7.
For 0 <t < 24 hours, the temperature inside a refrigerator in a kitchen is given by the function W that satisfies
3 cos t
dW
the differential equation
dt
W(t) is measured in degrees Celsius (°C), and t is measured in hours.
2W
At time t =
0 hours, the temperature inside the refrigerator is 3°C.
(a) Write an equation for the line tangent to the graph of y = W(t) at the point where t =
0. Use the equation
to approximate the temperature inside the refrigerator at t =
0.4 hour.
(b) Find y = W(t), the particular solution to the differential equation with initial condition W(0) = 3.
%3D
(c) The temperature in the kitchen remains constant at 20°C for 0 < t < 24. The cost of operating the
refrigerator accumulates at the rate of $0.001 per hour for each degree that the temperature in the kitchen
exceeds the temperature inside the refrigerator. Write, but do not evaluate, an expression involving an
integral that can be used to find the cost of operating the refrigerator for the 24-hour interval.
Transcribed Image Text:7. For 0 <t < 24 hours, the temperature inside a refrigerator in a kitchen is given by the function W that satisfies 3 cos t dW the differential equation dt W(t) is measured in degrees Celsius (°C), and t is measured in hours. 2W At time t = 0 hours, the temperature inside the refrigerator is 3°C. (a) Write an equation for the line tangent to the graph of y = W(t) at the point where t = 0. Use the equation to approximate the temperature inside the refrigerator at t = 0.4 hour. (b) Find y = W(t), the particular solution to the differential equation with initial condition W(0) = 3. %3D (c) The temperature in the kitchen remains constant at 20°C for 0 < t < 24. The cost of operating the refrigerator accumulates at the rate of $0.001 per hour for each degree that the temperature in the kitchen exceeds the temperature inside the refrigerator. Write, but do not evaluate, an expression involving an integral that can be used to find the cost of operating the refrigerator for the 24-hour interval.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning