When two people are dating, how one person feels often depends on how the other person feels. Your feelings are also informed by your own feelings, not just your partner's. In a certain well-known tragedy by Shakespeare, this feedback loop got way out of control.
In this lesson, students investigate the effect of coefficients on recursive functions. They first analyze a simpler version, where Romeo's feelings each week are simply scaled by Juliet's feelings the previous week. Then, they analyze a more complicated rule, where Romeo's feelings this week depend on both Juliet's and his own feelings the previous week. Can romantic love be modeled with mathematics? We're about to find out!