Explanation Given: The initial temperature of the roast is 20 ° F , while the oven is with a constant temperature 350 ° F . Theorem used: Separation of Variables: The solution of the differential equation, f ( y ) y ′ = g ( x ) is given implicitly by the equation, ∫ f ( y ) d y = ∫ g ( x ) d x . Formula used: Limited growth model: If the rate of change with respect to time t of a quantity y is proportional to the difference between y and a limiting value M , then y satisfies the differential equation, d y d t = k ( M − y ) , k > 0 , t > 0 Calculation: Let y represents the temperature of the roast at time t . Given that, the oven is maintained at a constant temperature of 350 ° F . Thus, the rate is proportional to the difference of the temperature and the limit 350 ° F . That is, d y d t = k ( y − 350 ) , k > 0 , t > 0 . Thus, the problem follows a limited growth model. Rewrite the differential equation d y d t = k ( y − 350 ) as follows. d y d t = k ( y − 350 ) 1 y − 350 d y = k d t The given differential equation d y d t = k ( y − 350 ) is in the form of f ( y ) y ′ = g ( x ) where, f ( y ) = 1 ( y − 350 ) and g ( t ) = k . By the above mentioned theorem, the solution is given by, ∫ f ( y ) d y = ∫ g ( t ) d t ∫ 1 ( y − 350 ) d y = ∫ k d t ln ( y − 350 ) = k t + C 1 e ln ( y − 350 ) = e k t + C 1 Simplify further as, y − 350 = e k t + C 1 y = 350 + e k t + C 1 y = 350 + C e k t , where C = e C 1 The roast is at 20 ° F and heated to 185 ° F after 1 hour

17th Edition

ISBN: 9781323520192

Author: Pearson

Publisher: PEARSON C

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 9.2, Problem 74E

To determine

To find: The temperature of the roast after 3 hours in the oven.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 73E

Chapter 9.2, Problem 75E

Students have asked these similar questions

4.1: 4) The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 4.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.5 centimeters and the area is 87 square centimeters?

Two populations of bacteria were given food treated with different vitamins to see how they would grow. Population A started with 900 bacteria and grew at a steady rate of 30 bacteria each hour, while Population B started with 450 bacteria and grew at a steady rate of 9% each hour. At what hour will Population B be larger than Population A? Select your answer from the choices below. a hour 12 b hour 9 c hour 11 d hour 10

my question is: If one earthquake has a magnitude of 5 on the Richter scale and a second earthquake has a magnitude of 6, what is the relationship between the intensities of the two earthquakes?

Chapter 9 Solutions

FIN 108 ISU LOOSE >IP<

Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MP Ch. 9.1 - Prob. 3MP Ch. 9.1 - Prob. 4MP Ch. 9.1 - Prob. 5MP Ch. 9.1 - Prob. 1ED Ch. 9.1 - Prob. 2ED Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The temperature of the roast after 3 hours in the oven.

Solution Summary: Theorem used: Separation of Variables: The solution of the differential equation is given implicitly by the equation.

Concept explainers

Videos

To find: The temperature of the roast after 3 hours in the oven.

Want to see the full answer?

Chapter 9 Solutions