Questions: One who is exercising should not exceed his or her maximum heart rate, which is determined basis of that person's gender, age, and resting heart rate. The table relates resting heart rate ximum heart rate for a 20-year-old man. Use a graphing calculator to model the data with a linear function. Estimate the maximum heart rate if the resting heart rate is 42, 62, 74, and 82. What is the correlation coefficient? How confident are you about using the regression line to estimate function values? Resting Heart Rate, H (in beats per minute) Maximum Heart Rate, M (in beats per minute) 50 160 60 160 70 160 80 170 The linear function that best models the data is M=0.3 H+148. The estimated maximum heart rate for the resting heart rate of 42 is beats per minute.

One who is exercising should not exceed his or her maximum heart rate, which is determined basis of that person's gender, age, and resting heart rate. The table relates resting heart rate ximum heart rate for a 20-year-old man. Use a graphing calculator to model the data with a linear function. Estimate the maximum heart rate if the resting heart rate is 42, 62, 74, and 82. What is the correlation coefficient? How confident are you about using the regression line to estimate function values? Resting Heart Rate, H (in beats per minute) Maximum Heart Rate, M (in beats per minute) 50 160 60 160 70 160 80 170 The linear function that best models the data is M=0.3 H+148. The estimated maximum heart rate for the resting heart rate of 42 is beats per minute.
Transcript text: One who is exercising should not exceed his or her maximum heart rate, which is determined basis of that person's gender, age, and resting heart rate. The table relates resting heart rate ximum heart rate for a 20 -year-old man. Use a graphing calculator to model the data with a linear function. Estimate the maximum heart rate if the resting heart rate is $42,62,74$, and 82. What is the correlation coefficient? How confident are you about using the regression line to estimate function values? \begin{tabular}{|c|r|} \hline \begin{tabular}{c} Resting Heart Rate, H \\ (in beats per minute) \end{tabular} & \begin{tabular}{r} Maximum H \\ M \end{tabular} \\ & (in beats p \\ \hline 50 & 16 \\ \hline 60 & 16 \\ \hline 70 & 16 \\ \hline 80 & 17 \\ \hline \end{tabular} The linear function that best models the data is $M=0.3 H+148$. The estimated maximum heart rate for the resting heart rate of 42 is $\square$ beats per minute.
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Solution

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Solution Steps

To solve this problem, we need to use the given linear function \( M = 0.3H + 148 \) to estimate the maximum heart rate for the given resting heart rates. We will substitute the given resting heart rates into the linear function to find the corresponding maximum heart rates.

Solution Approach
  1. Use the linear function \( M = 0.3H + 148 \).
  2. Substitute the given resting heart rates (42, 62, 74, and 82) into the function to calculate the maximum heart rates.
  3. Output the results.
Step 1: Define the Linear Function

The linear function that models the data is given by: \[ M = 0.3H + 148 \] where \( M \) is the maximum heart rate and \( H \) is the resting heart rate.

Step 2: Substitute Resting Heart Rates into the Function

We substitute the given resting heart rates \( H = 42, 62, 74, 82 \) into the linear function to find the corresponding maximum heart rates.

Step 3: Calculate the Maximum Heart Rates

For \( H = 42 \): \[ M = 0.3 \times 42 + 148 = 160.6 \]

For \( H = 62 \): \[ M = 0.3 \times 62 + 148 = 166.6 \]

For \( H = 74 \): \[ M = 0.3 \times 74 + 148 = 170.2 \]

For \( H = 82 \): \[ M = 0.3 \times 82 + 148 = 172.6 \]

Final Answer

The estimated maximum heart rates for the given resting heart rates are:

  • For \( H = 42 \) bpm, \( M = \boxed{160.6} \) bpm.
  • For \( H = 62 \) bpm, \( M = \boxed{166.6} \) bpm.
  • For \( H = 74 \) bpm, \( M = \boxed{170.2} \) bpm.
  • For \( H = 82 \) bpm, \( M = \boxed{172.6} \) bpm.
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