The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age, \( 220-\mathrm{a} \). Your exercise goal is to improve cardiovascular conditioning. Use the following formulas to answer parts (a) and (b). Lower limit of range \( \quad \mathrm{H}=\frac{7}{10}(220-\mathrm{a}) \) Upper limit of range \( \quad \mathrm{H}=\frac{4}{5}(220-\mathrm{a}) \) The lower limit of the heart range is 132 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 31-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.)

To find the upper limit of the heart range for a 31-year-old with the exercise goal, we need to substitute the age into the formula for the upper limit of the heart range. Given: - Lower limit of the heart range: \( H = \frac{7}{10}(220 - a) \) - Upper limit of the heart range: \( H = \frac{4}{5}(220 - a) \) - Age: \( a = 31 \) Substitute the age into the formula for the upper limit of the heart range: \[ H = \frac{4}{5}(220 - 31) \] Now, we can calculate the upper limit of the heart range for a 31-year-old with this exercise goal. Calculate the value by following steps: - step0: Calculate: \(\frac{4}{5}\left(220-31\right)\) - step1: Subtract the numbers: \(\frac{4}{5}\times 189\) - step2: Multiply: \(\frac{4\times 189}{5}\) - step3: Multiply: \(\frac{756}{5}\) The upper limit of the heart range for a 31-year-old with this exercise goal is 151.2 beats per minute. Rounding to the nearest integer, the upper limit of the heart range is 151 beats per minute.