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

Lower limit of range:

[tex]
H=\frac{7}{10}(220-a) \\
H=\frac{4}{5}(220-a)
[/tex]

a. What is the lower limit of the heart range, in beats per minute, for a 41-year-old with this exercise goal?

The lower limit of the heart range is [tex]$\square$[/tex] beats per minute.
(Round to the nearest integer as needed.)



Answer :

GinnyAnswer
To find the lower limit of the heart rate range for a 41-year-old exercising to improve cardiovascular conditioning, follow these steps:

1. Determine the maximum heart rate (MHR):
The maximum heart rate is calculated as [tex]\(220\)[/tex] minus the person's age.
[tex]\[ \text{MHR} = 220 - \text{age} \][/tex]
For a 41-year-old:
[tex]\[ \text{MHR} = 220 - 41 \][/tex]
[tex]\[ \text{MHR} = 179 \text{ beats per minute (bpm)} \][/tex]

2. Calculate the lower limit of the heart rate range:
The lower limit is given by the formula:
[tex]\[ H_{\text{lower}} = \frac{7}{10} \times (220 - a) \][/tex]
Substitute [tex]\(a = 41\)[/tex]:
[tex]\[ H_{\text{lower}} = \frac{7}{10} \times (220 - 41) \][/tex]
[tex]\[ H_{\text{lower}} = \frac{7}{10} \times 179 \][/tex]
[tex]\[ H_{\text{lower}} = 0.7 \times 179 \][/tex]

3. Multiply to find the exact value:
[tex]\[ H_{\text{lower}} = 125.3 \text{ bpm} \][/tex]

4. Round to the nearest integer:
Rounding 125.3 to the nearest integer gives 125.

Therefore, the lower limit of the heart range for a 41-year-old is [tex]\(125\)[/tex] beats per minute.

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