The target training heart rate is a useful measure of exercise intensity, which is used by everyone from athletes to patients recovering from heart attacks. The Karvonen formula is commonly used to determine a target training heart rate when exercising. This formula takes into consideration both the age of the person training as well as their resting heart rate.

Using this formula, the maximum heart rate (HR_max) is computed as,

HR_max = 220 − A,

where A represents the age of the person training. The reserve heart rate (HR_rsv) is computed as,

HR_rsv = HR_max− HR_rest,

where HR_rest is the resting heart rate in beats per minute (bpm). Using these measures, the target heart rate (HR_targ) is computed as,

HR_targ = p · HR_rsv + HR_rest,

where p is the training percentage. Depending on the specific training goals, p is commonly between 50% and 85% (0.50 - 0.85) when exercising. In practice, lower values of p correspond to an intensity of exercise consistent with health maintenance and weight loss while higher values of p correspond to an exercise intensity compatible with intense fitness training.

Use the above equations to answer the following questions:

Calculate the target heart rate given the resting heart rate and training goal.

Determine the resting heart rate given the target heart rate and training goal.

Calculate the target heart rate given the training goal and resting heart rate.

Determine the reserve heart rate given the resting heart rate and training goal.

Rewrite the equation for the target heart rate.

Find the slope of the line for the equation for determining the target heart rate.

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