A family driving across Canada in the summer experienced a delay when their motor home's engine overheated to 200°C. After waiting 7 minutes in the scorching 45°C heat, they checked the engine's temperature and discovered it had cooled to 160°C. The engine must cool to 70°C before they can resume driving. The change in temperature of the motor home's engine follows Newton's law of cooling, represented by the exponential relationship, T – T; = (To – T5)ekt, in which T'is the object's temperature at time t, T, is the temperature of the surroundings, To is the initial temperature of the object, and k is a constant representing the relative rate of cooling of the given object. If the temperature difference between the engine and the air outside changes at a rate proportional to this temperature difference, then what is the rate of decrease of the engine's temperature at the instant when the family can get moving again? . a) Step 1: State the exponential function that represents the motor home's engine temperature after time t. (Solve for k) b) Step 2: Determine the timet when T= 70°C. c) Step 3: Find the rate of change of the motor home's engine temperature. d) Interpret the meaning of your answer in part c), in the context of the question.
A family driving across Canada in the summer experienced a delay when their motor home's engine overheated to 200°C. After waiting 7 minutes in the scorching 45°C heat, they checked the engine's temperature and discovered it had cooled to 160°C. The engine must cool to 70°C before they can resume driving. The change in temperature of the motor home's engine follows Newton's law of cooling, represented by the exponential relationship, T – T; = (To – T5)ekt, in which T'is the object's temperature at time t, T, is the temperature of the surroundings, To is the initial temperature of the object, and k is a constant representing the relative rate of cooling of the given object. If the temperature difference between the engine and the air outside changes at a rate proportional to this temperature difference, then what is the rate of decrease of the engine's temperature at the instant when the family can get moving again? . a) Step 1: State the exponential function that represents the motor home's engine temperature after time t. (Solve for k) b) Step 2: Determine the timet when T= 70°C. c) Step 3: Find the rate of change of the motor home's engine temperature. d) Interpret the meaning of your answer in part c), in the context of the question.
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...
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Transcribed Image Text:A family driving across Canada in the summer experienced a delay when their motor home's engine overheated to 200°C.
After waiting 7 minutes in the scorching 45°C heat, they checked the engine's temperature and discovered it had cooled
to 160°C. The engine must cool to 70°C before they can resume driving.
The change in temperature of the motor home's engine follows Newton's law of cooling, represented by the exponential
relationship, T – T; = (To – T5)ekt, in which T'is the object's temperature at time t, T, is the temperature of the
surroundings, To is the initial temperature of the object, and k is a constant representing the relative rate of cooling of the
given object.
If the temperature difference between the engine and the air outside changes at a rate proportional to this temperature
difference, then what is the rate of decrease of the engine's temperature at the instant when the family can get moving
again?
. a) Step 1: State the exponential function that represents the motor home's engine temperature after time t.
(Solve for k)
b) Step 2: Determine the timet when T= 70°C.
c) Step 3: Find the rate of change of the motor home's engine temperature.
d) Interpret the meaning of your answer in part c), in the context of the question.
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