In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for understanding infinite series and growth functions later in the course sequence. Students further explore interconnections between such functions, culminating in the synthesis of the Euler formula. These activities have been implemented over several years with encouraging results.