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Newton's Law of Cooling A cheesecake is taken out of the oven with an ideal internal temperature of 165°F, and is placed into a 35°F refrigerator. After 10 minutes, the cheesecake has cooled to 150°F. If we must wait until the cheesecake has cooled to 70°F before we eat it, how long will we have to wait? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the period where the temperature will be 700 F. 7. Graph the solutions My Solutions >

Newton's Law of Cooling A cheesecake is taken out of the oven with an ideal internal temperature of 165°F, and is placed into a 35°F refrigerator. After 10 minutes, the cheesecake has cooled to 150°F. If we must wait until the cheesecake has cooled to 70°F before we eat it, how long will we have to wait? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the period where the temperature will be 700 F. 7. Graph the solutions My Solutions >

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Newton's Law of Cooling My Solutions > A cheesecake is taken out of the oven with an ideal internal temperature of 165°F, and is placed into a 35°F refrigerator. After 10 minutes, the cheesecake has cooled to 150°F. If we must wait until the cheesecake has cooled to 70°F before we eat it, how long will we have to wait? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the period where the temperature will be 700 F. 7. Graph the solutions
Transcribed Image Text:Newton's Law of Cooling My Solutions > A cheesecake is taken out of the oven with an ideal internal temperature of 165°F, and is placed into a 35°F refrigerator. After 10 minutes, the cheesecake has cooled to 150°F. If we must wait until the cheesecake has cooled to 70°F before we eat it, how long will we have to wait? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the period where the temperature will be 700 F. 7. Graph the solutions
1 %Setup the variables U(t) as the function of Temperature over a period of time t, and k that will be used in the program. 2 %Find also the derivative of P(t) and set as dP 3 4 5 6 %Initial Conditions 7 8 9 Ta= %Ambient Temperature 10 Ufinal = %Final Temperature 11 12 %Set the differential equation model as eqn1; 13 14 15 %Find k1 and k2, by solving the initial value problem eqn1 using cond1 and cond2, respectively. 16 17 18 19 %Solve for k by equating k1 and k2 at t=0. Save results as k. 20 21 22 %Solve the eqn1 using the acquired value of k and using Initial value cond1. 23 24 25 %Let the Usoln be equal to Ufinal. Solve the equation and save your answer as tfinal 26 27 28 29 % Plot the equation: Use the Title=Cake Temperature, XValue=Time (in Minutes), YValue=Temperature (F) 30 31 32 33 %Use the domain (0, tfinal+5) with e.2 gaps from each point 34 x=0:0.2:tfinal+20; 35 36 37 38 39 40 41 plot (0,Usoln(0), 'r*'); 42 plot (tfinal,Usoln(tfinal), 'r*'); 43 hold off;
Transcribed Image Text:1 %Setup the variables U(t) as the function of Temperature over a period of time t, and k that will be used in the program. 2 %Find also the derivative of P(t) and set as dP 3 4 5 6 %Initial Conditions 7 8 9 Ta= %Ambient Temperature 10 Ufinal = %Final Temperature 11 12 %Set the differential equation model as eqn1; 13 14 15 %Find k1 and k2, by solving the initial value problem eqn1 using cond1 and cond2, respectively. 16 17 18 19 %Solve for k by equating k1 and k2 at t=0. Save results as k. 20 21 22 %Solve the eqn1 using the acquired value of k and using Initial value cond1. 23 24 25 %Let the Usoln be equal to Ufinal. Solve the equation and save your answer as tfinal 26 27 28 29 % Plot the equation: Use the Title=Cake Temperature, XValue=Time (in Minutes), YValue=Temperature (F) 30 31 32 33 %Use the domain (0, tfinal+5) with e.2 gaps from each point 34 x=0:0.2:tfinal+20; 35 36 37 38 39 40 41 plot (0,Usoln(0), 'r*'); 42 plot (tfinal,Usoln(tfinal), 'r*'); 43 hold off;
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