Question

the maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age, ( 220 - a ). your exercise goal is to improve cardiovascular conditioning. use the following formulas to answer parts (a) and (b).

lower limit of range ( h = \frac{7}{10}(220 - a) )

upper limit of range ( h = \frac{4}{5}(220 - a) )

a. what is the lower limit of the heart range, in beats per minute, for a 37-year-old with this exercise goal?

the lower limit of the heart range is 128 beats per minute

(round to the nearest integer as needed.)

b. what is the upper limit of the heart range, in beats per minute, for a 37-year-old with this exercise goal?

thus, the upper limit of the heart range is (square) beats per minute

(round to the nearest integer as needed.)

Explanation:

Step1: Identify the formula and age

The formula for the upper limit of the heart rate range is \( H=\frac{4}{5}(220 - a) \), and the age \( a = 37 \).

Step2: Calculate \( 220 - a \)

Substitute \( a = 37 \) into \( 220 - a \): \( 220 - 37=183 \).

Step3: Calculate the upper limit

Substitute \( 220 - a = 183 \) into the formula \( H=\frac{4}{5}(220 - a) \): \( H=\frac{4}{5}\times183 \).
First, calculate \( 4\times183 = 732 \), then divide by 5: \( \frac{732}{5}=146.4 \).

Step4: Round to the nearest integer

Rounding \( 146.4 \) to the nearest integer gives \( 146 \).

Answer:

146