Questions: The temperature of an automobile engine is 7° Celsius when the engine is started and 79° nine minutes later. Use a linear model to predict the engine temperature for both two minutes and two hours after it started. Are your predictions reasonable? 2 minutes: 2 hours:

The temperature of an automobile engine is 7° Celsius when the engine is started and 79° nine minutes later. Use a linear model to predict the engine temperature for both two minutes and two hours after it started. Are your predictions reasonable? 2 minutes: 2 hours:
Transcript text: The temperature of an automobile engine is $7^{\circ}$ Celsius when the engine is started and $79^{\circ}$ nine minutes later. Use a linear model to predict the engine temperature for both two minutes and two hours after it started. Are your predictions reasonable? 2 minutes: $\square$ 2 hours: $\square$
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Solution

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Solution Steps

Step 1: Determine the Rate of Temperature Change

The initial temperature of the engine is \( 7^{\circ} \) Celsius, and after \( 9 \) minutes, the temperature rises to \( 79^{\circ} \) Celsius. The rate of temperature change per minute can be calculated as follows:

\[ \text{Rate of Change} = \frac{79 - 7}{9} = 8 \, \text{degrees Celsius per minute} \]

Step 2: Predict the Temperature at 2 Minutes

Using the rate of change, we can predict the temperature of the engine after \( 2 \) minutes:

\[ \text{Temperature at 2 minutes} = 7 + (8 \times 2) = 23^{\circ} \, \text{Celsius} \]

Step 3: Predict the Temperature at 2 Hours

Next, we predict the temperature of the engine after \( 2 \) hours, which is \( 120 \) minutes:

\[ \text{Temperature at 120 minutes} = 7 + (8 \times 120) = 967^{\circ} \, \text{Celsius} \]

Final Answer

The predicted temperatures are:

  • At \( 2 \) minutes: \( \boxed{23^{\circ}} \)
  • At \( 2 \) hours: \( \boxed{967^{\circ}} \)

These predictions indicate that while the temperature at \( 2 \) minutes seems reasonable, the temperature at \( 2 \) hours is unreasonably high for an automobile engine.

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