Concern the maximum heart rate (MHR), which is the maximum number of times a person’s heart can safely beat in one minute. If MHR is in beats per minute and a is age in years, the formulas used to estimate MHR are

Recently it has been suggested that a more accurate predictor of MHR for both males and females is given by

MHR = 208 − 0.7a.

(a) At what age do the old and new formulas give the same MHR for females? For males?

(b) Which of the following is true? 

(i) The new formula predicts a higher MHR for young people and a lower MHR for older people than the old formula. 

(ii) The new formula predicts a lower MHR for young people and a higher MHR for older people than the old formula. 

(c) When testing for heart disease, doctors ask patients to walk on a treadmill while the speed and incline are gradually increased until their heart rates reach 85 percent of the MHR. For a 65-year-old male, what is the difference in beats per minute between the heart rate reached if the old formula is used and the heart rate reached if the new formula is used?

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For females: MHR = 226 - a, For males: MHR = 220 - a.