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The scatterplot below shows the temperatures of a cup of hot cocoa after it is poured into a serving cup. The hot cocoa starts at approximately 180º F, but the temperature decreases over time.Use the graph and trend line equation, 𝑦=171.46𝑒−0.012𝑥 , to estimate the temperature of the hot cocoa after 38 minutes.(Round your answer to the nearest whole degree)

Question

The scatterplot below shows the temperatures of a cup of hot cocoa after it is poured into a serving cup. The hot cocoa starts at approximately 180º F, but the temperature decreases over time.Use the graph and trend line equation, 𝑦=171.46𝑒−0.012𝑥 , to estimate the temperature of the hot cocoa after 38 minutes.(Round your answer to the nearest whole degree)

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Solution

To estimate the temperature of the hot cocoa after 38 minutes using the given trend line equation, follow these steps:

  1. Identify the equation: The equation given is 𝑦=171.46𝑒−0.012𝑥. In this equation, 'y' represents the temperature of the hot cocoa and 'x' represents the time in minutes.

  2. Substitute the value of 'x': Since we want to find the temperature after 38 minutes, we substitute x = 38 into the equation. This gives us 𝑦=171.46𝑒−0.012(38).

  3. Solve the equation: Now, we need to solve this equation to find 'y'. This involves multiplying -0.012 by 38 and then taking e to the power of this result. After that, we multiply the outcome by 171.46.

  4. Round the result: Once we have the value of 'y', we round it to the nearest whole degree as the question instructs.

Please note that you'll need a calculator that can handle exponential functions to solve this equation.

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