CAREER LINK WRAP-UP |Investigate and Apply CHAPTER 1: ASSESSING ATHLETIC PERFORMANCE An Olympic coach has developed a 6 min fitness test for her team members that sets target values for heart rates. The monitor they have available counts the total number of heartbeats, starting from a rest position at "time zero." The results for one of the team members are given in the table below. Number of Time (min) Heartbeats 0.0 0 1.0 55 2.0 120 3.0 195 4.0 280 5.0 375 6.0 480 a. The coach has established that each athlete's heart rate must not exceed 100 beats per minute at exactly 3 min. Using a graphical technique, determine if this athlete meets the coach's criterion. b. The coach needs to know the instant in time when an athlete's heart rate actually exceeds 100 beats per minute. Explain how you would solve this problem graphically. Is a graphical solution an efficient method? Explain. How is this problem different from part a? c. Build a mathematical model with the total number of heartbeats as a function of time (n = f(t)). First determine the degree of the polynomial, and then use a graphing calculator to obtain an algebraic model. d. Solve part b algebraically by obtaining an expression for the instantaneous rate of change in the number of heartbeats (heart rate) as a function of time (r = g(t)) using the methods presented in the chapter. Compare the accuracy and efficiency of solving this problem graphically and algebraically