During exercise, the recommended maximum heart rate in beats per minute is modeled by the formula M = 176 − 0.8A, where M is the maximum heart rate and A is the person’s age. Solve the formula for A. At what age would you have a recommended maximum heart rate in beats per minute of 140?

1. To solve the formula [tex]M=176-0.8A[/tex] for A, the first thing we are going to do is subtract M for both sides of the equation:
[tex]M-M=176-0.8A-M[/tex]
[tex]0=176-0.8A-M[/tex]
Next, we are going to add 0.8A to both sides of the equation:
[tex]0.8A=176-0.8A+0.8A-M[/tex]
[tex]0.8A=176-M[/tex]
Finally, we are going to divide both sides of the equation by 0.8:
[tex] \frac{0.8A}{0.8} = \frac{176-M}{0.8} [/tex]
[tex]A= \frac{176-M}{0.8} [/tex]

2. Now, to find at what age the maximum heart rate in beats per minute should be 140, we are going to replace M with 140 in our formula:
[tex]A= \frac{176-140}{0.8} [/tex]
[tex]A= \frac{36}{0.8} [/tex]
[tex]A=45[/tex]

We can conclude that 45 years old person, must not exceed a heart rate of 140 beats per minute during exercise.