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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)[/tex]

Upper limit of range: [tex]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 125 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 41-year-old with this exercise goal?

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



Answer :

GinnyAnswer
Let's break down the solution step-by-step for a 41-year-old with a given exercise goal:

First, we are given the formulas to determine the lower and upper limits of the heart rate range during exercise, based on the person's age. The formulas are as follows:
- Lower limit of range: [tex]\( H = \frac{7}{10} \times (220 - a) \)[/tex]
- Upper limit of range: [tex]\( H = \frac{4}{5} \times (220 - a) \)[/tex]

Where [tex]\(a\)[/tex] is the age of the person.

1. Determine the maximum heart rate:

The maximum heart rate is calculated by subtracting the person's age from 220:
[tex]\[ 220 - 41 = 179 \text{ beats per minute} \][/tex]

2. Calculate the lower limit of the heart rate range:

Using the given formula for the lower limit:
[tex]\[ H = \frac{7}{10} \times 179 \][/tex]
Evaluating this expression:
[tex]\[ H = 0.7 \times 179 = 125.3 \][/tex]
Rounding 125.3 to the nearest integer, we get:
[tex]\[ 125 \text{ beats per minute} \][/tex]

Therefore, the lower limit of the heart rate range for a 41-year-old is approximately 125 beats per minute.

3. Calculate the upper limit of the heart rate range:

Using the given formula for the upper limit:
[tex]\[ H = \frac{4}{5} \times 179 \][/tex]
Evaluating this expression:
[tex]\[ H = 0.8 \times 179 = 143.2 \][/tex]
Rounding 143.2 to the nearest integer, we get:
[tex]\[ 143 \text{ beats per minute} \][/tex]

Therefore, the upper limit of the heart rate range for a 41-year-old is approximately 143 beats per minute.

In conclusion:
- The lower limit of the heart range for a 41-year-old is 125 beats per minute.
- The upper limit of the heart range for a 41-year-old is 143 beats per minute.