5. 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 – Tg = (To – T3)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. *Hint: solve for k b) Step 2: Determine the time t when T=70°C. c) Step 3: Find the rate of change of the motor home's engine temperature.
5. 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 – Tg = (To – T3)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. *Hint: solve for k b) Step 2: Determine the time t when T=70°C. c) Step 3: Find the rate of change of the motor home's engine temperature.
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Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in complete sentences and therefore statements.
Transcribed Image Text:Answer the question in FULL details. Show ALL your steps and work in your calculations.
Answer in complete sentences and therefore statements.
5. 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 – T3)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.
*Hint: solve for k
b) Step 2: Determine the time t 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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