The volume of air in an athlete's lungs can be modeled by the equation v = 477 sin(87t) + 790, where v is in cubic centimeters and t is in minutes. The maximum volume is 477 cc, the minimum is 313 cc, and the athlete takes 87 breaths per minute.
The equation is v = 477 sin(87t) + 790, where v is the volume of air in cubic centimeters and t is the time in minutes. The sine function in the equation means that the volume of air in the athlete's lungs oscillates back and forth over time. The amplitude of the oscillation is 477 cubic centimeters, which is the maximum amount of air that the athlete's lungs can hold. The average volume of air in the athlete's lungs is 790 cubic centimeters.
The questions on the image ask about the maximum and minimum possible volume of air in the athlete's lungs, as well as how many breaths the athlete takes per minute.
The maximum possible volume of air in the athlete's lungs is 477 cubic centimeters, as I mentioned before. This occurs when the sine function in the equation is equal to 1. The minimum possible volume of air in the athlete's lungs is 313 cubic centimeters, which occurs when the sine function in the equation is equal to -1.
The number of breaths that the athlete takes per minute is equal to the frequency of the sine function in the equation. The frequency of a sine function is the number of times that it completes a cycle in a given unit of time. The frequency of the sine function in the equation is 87 cycles per minute. So, the athlete takes 87 breaths per minute.