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D I Til and placed it in an oven set to 200° C. After ten minutes she checks the quiche and it has a temperature of T = 20°C. The rate that the temperature of the quiche increa is proportional to the difference in temperature between the oven and the quiche. Write a differential equation to model this scenario and use it to show that T 200 + Ae-kt. Find the value of k in exact form. The quiche is ready when the internal temperature reaches 60° C. How much longe

D I Til and placed it in an oven set to 200° C. After ten minutes she checks the quiche and it has a temperature of T = 20°C. The rate that the temperature of the quiche increa is proportional to the difference in temperature between the oven and the quiche. Write a differential equation to model this scenario and use it to show that T 200 + Ae-kt. Find the value of k in exact form. The quiche is ready when the internal temperature reaches 60° C. How much longe

Advanced Engineering Mathematics
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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(i) (ii) (iii) Megan has taken a frozen quiche from the freezer with an initial temperature T = 0°C and placed it in an oven set to 200° C. After ten minutes she checks the quiche and now it has a temperature of T = 20°C. The rate that the temperature of the quiche increases is proportional to the difference in temperature between the oven and the quiche. Write a differential equation to model this scenario and use it to show that 200 + Ae-kt. T = Find the value of k in exact form. The quiche is ready when the internal temperature reaches 60° C. How much longer after Megan checked the quiche will it be ready? Answer to the nearest minute.
Transcribed Image Text:(i) (ii) (iii) Megan has taken a frozen quiche from the freezer with an initial temperature T = 0°C and placed it in an oven set to 200° C. After ten minutes she checks the quiche and now it has a temperature of T = 20°C. The rate that the temperature of the quiche increases is proportional to the difference in temperature between the oven and the quiche. Write a differential equation to model this scenario and use it to show that 200 + Ae-kt. T = Find the value of k in exact form. The quiche is ready when the internal temperature reaches 60° C. How much longer after Megan checked the quiche will it be ready? Answer to the nearest minute.
Expert Solution
Step 1

Let the temperature of the quiche at time 't' be 'T'

Given rate of temperature of the quiche is proportional to difference of temperature of oven and the quiche.

Temperature of the oven is 2000C

hence

dTdt∝(T-200)

or

dTdt=-k(T-200)

where -k is proportionality constant.

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