To find the lower limit of the heart rate range for a 25-year-old, we use the following formula:
[tex]\[ H = \frac{7}{10}(220 - a) \][/tex]
where [tex]\( a \)[/tex] is the age in years.
Step-by-step solution:
1. Identify the given values:
- The age ([tex]\( a \)[/tex]) is 25 years.
2. Substitute the age into the formula:
[tex]\[ H = \frac{7}{10}(220 - 25) \][/tex]
3. Calculate the expression inside the parentheses first:
[tex]\[ 220 - 25 = 195 \][/tex]
4. Substitute this value back into the formula:
[tex]\[ H = \frac{7}{10} \times 195 \][/tex]
5. Simplify the multiplication:
[tex]\[ H = 0.7 \times 195 \][/tex]
6. Calculate the result:
[tex]\[ H = 136.5 \][/tex]
7. Round the result to the nearest integer:
[tex]\[ H \approx 136 \][/tex]
Thus, the lower limit of the heart range for a 25-year-old is 136 beats per minute.
