Final answer:
The initial volume of the athlete's lungs is 500 cubic centimeters. The time it takes for the lungs to be empty can be found by solving the quadratic equation 0 = 500 + 120t - 5t^2 for the variable t and selecting the positive solution.
Step-by-step explanation:
The volume of air contained in the athlete's lungs as modeled by the equation V(t) = 500 + 120t - 5t2 can be analyzed to find (a) the initial volume of air and (b) the time it takes for the lungs to be empty.
Initial volume (a)
The initial volume is calculated by evaluating the equation at time t = 0, which results in V(0) = 500 + 120(0) - 5(0)2 = 500 cubic centimeters. Therefore, the initial volume of air in the athlete's lungs is 500 cubic centimeters.
Time to empty lungs (b)
To find the time when the athlete's lungs will be empty, we need to solve for t when V(t) = 0. We set up the equation 0 = 500 + 120t - 5t2 and solve for t, which may require the use of factoring or the quadratic formula. The positive value of t obtained will be the time in minutes when the lungs are empty.