An introduction to an application task.
In a calculus application task that combines bungee jumping and ski resort turning points, students can explore the concepts of piecewise functions, continuity, and graphing using a TI-Nspire CAS calculator. First, they can create a piecewise function that models the height of a bungee jumper as a function of time, incorporating different phases like free fall and the rebound. Then, they can analyze the function to find turning points that represent key moments during the jump. Next, they can introduce another piecewise function to represent the elevation of a ski resort trail, potentially including sections with varying slopes. By graphing both functions on the TI-Nspire CAS, students can examine continuity at points where the bungee jumper’s path intersects the ski resort trail, allowing them to determine if there are any potential safety concerns or thrilling moments of excitement for skiers and jumpers alike. This task not only reinforces calculus concepts but also illustrates their practical relevance in real-world scenarios.