Find the training heart rate function, T(M), for a person with a resting heart r

Question

Find the training heart rate function, T(M), for a person with a resting heart rate of 76 beats per minute, then find the following to the nearest whole number. T(M) = Find the maximum heart rate function, M(x), for a person x years of age. M(x) = What is the maximum heart rate for a 23-year-old person? beats per minute What is the training heart rate for a 23-year-old person with a resting heart rate of 76 beats per minute? Round to the nearest whole number. beats per minute What is the training heart rate for a 30-year-old person with a resting heart rate of 76 beats per minute? Round to the nearest whole number. beats per minute What is the training heart rate for a 40-year-old person with a resting heart rate of 76 beats per minute? Round to the nearest whole number. beats per minute

Explanation / Answer

The training heart rate function T(M) = R+0.6[M(x)R], where R = resting heart rate, M(x) = maximum heart rate, and x = age. Also, M(x) i.e. the maximum heart rate = 220-x.

(a) The maximum heart rate for a person x years of age is M(x) = 220-x.

(b) The maximum heart rate for a 23 year old person is 220-23 = 197.

(c) The training heart rate for a x year old person with a resting heart rate of R beats per minute is given by R+0.6[M(x)R]. Here,T(M) = 76 + 0.6(197-76) = 76+0.6(121) = 76+ 72.6 = 148.6= 149          ( on rounding off to the nearest whole number).

(d) The training heart rate for a 30 year old person with a resting heart rate of 76 beats per minute is

76 + 0.6(220-30-76) = 76 + 0.6(114) = 76 + 68.4 = 144.4 = 144 ( on rounding off to the nearest whole number).

(e) The training heart rate for a 40 year old person with a resting heart rate of 76 beats per minute is

76 + 0.6(220-40-76) = 76+ 0.6(104) = 76+62.4 = 138.4 = 138( on rounding off to the nearest whole number).

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