Consider a 35°F object placed in a 64°F room. a. Write a differential equation for T, the temperature of the object at time t, using k > 0 for the constant of proportionality, and wri your equation in terms of T, k, and t. T' = k(T-1) b. Give the general solution to the differential equation found in Part a. Simplify your solution in terms of an unspecified constant C appears as the coefficient of an exponential term and the constant of proportionality k. T = c. The temperature of the object is 35°F initially and 42°F one hour later. Find the temperature of the object after 3 hours. T(3) = degrees F
Consider a 35°F object placed in a 64°F room. a. Write a differential equation for T, the temperature of the object at time t, using k > 0 for the constant of proportionality, and wri your equation in terms of T, k, and t. T' = k(T-1) b. Give the general solution to the differential equation found in Part a. Simplify your solution in terms of an unspecified constant C appears as the coefficient of an exponential term and the constant of proportionality k. T = c. The temperature of the object is 35°F initially and 42°F one hour later. Find the temperature of the object after 3 hours. T(3) = degrees F
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider a 35°F object placed in a 64°F room.
a. Write a differential equation for T, the temperature of the object at time t, using k > 0 for the constant of proportionality, and write
your equation in terms of T, k, and t.
T' = k(T-1)
b. Give the general solution to the differential equation found in Part a. Simplify your solution in terms of an unspecified constant C that
appears as the coefficient of an exponential term and the constant of proportionality k.
T =
The
temperature of the object is 35°F initially and 42°F one hour later. Find the temperature of the object after 3 hours.
С.
Т(3)
degrees F
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