Question

Use the following formulas to answer the questions below:T(M,R) = R +0.6(M-R)M(x) = 220 - 2where R-resting heart rate, M = maximum heart rate, and x = ageRecall our discussion of heart rate and composition of functions from the end of the section. Find the trainingheart rate function, T(M) for a person with a resting heart rate of 62 beats per minute, then find the following.a. Find the maximum heart rate function, M(x) for a person 2 years of age.M(x) =_____b. What is the maximum heart rate for a 21-year-old person?The max heart rate for a 21 - year-old person is ____ beats per minute.c. What is the training heart rate for a 21-year-old person with a resting heart rate of 62 beats per minute?The training heart rate for a 21-year-old person with a resting heart rate of 62 beats per minute isper minute.beatsd. What is the training heart rate for a 27-year-old person with a resting heart rate of 62 beats per minute?The training heart rate for a 27-year-old person with a resting heart rate of 62 beats per minute is beatsper minutee. What is the training heart rate for a 36-year-old person with a resting heart rate of 62 beats per minute?The training heart rate for a 36-year-old person with a resting heart rate of 62 beats per minute is beatsper minute.

Answer 1

item (a):

The function for the maximum heart rate as a function of x(years of age) is already given, and it is

`M(x)=220-x`

item (b):

On the previous item we got a function for the maximum heart rate with the age as the argument. For a 21-year-old person, the maximum heart rate is given by evaluating x = 21 on the function.

`M(21)=220-21=199`

The max heart rate for a 21 - year-old person is 199 beats per minute.

item (c):

The training heart rate is given by the following function

`T(M,R)=R+0.6(M-R)`

where M represents the maximum heart rate and R represents the resting heart rate.

The max heart rate for a 21 - year-old person was calculated on the previous item, and it is 199. The given resting rate is 62 beats per minute. Now that we have those two values, we can evaluate them on the training heart rate function

`T(199,62)=62+0.6(199-62)=144.2`

The training heart rate for a 21-year-old person with a resting heart rate of 62 beats per minute is 144.2 per minute.

item (d):

Again, we just need to evaluate the corresponding max heart race of a 27 years old with a resting rate of 62 beats per minute on the training heart rate function.

First, we calculate the max heart rate using the function from item (a):

`M(27)=220-27=193`

Now, using those values on the training heart rate function, we have

`M(193,62)=62+0.6(193-62)=140.6`

The training heart rate for a 27-year-old person with a resting heart rate of 62 beats per minute is beats 140.6 per minute.

item (e):

Analogously to the previous item

`M(36)=220-36=184`

evaluating on the training heart function

`T(184,62)=62+0.6(184-62)=135.2`

The training heart rate for a 36-year-old person with a resting heart rate of 62 beats per minute is beats 135.2 per minute.