When teaching arithmetic and geometric sequences in Algebra, I commonly start the lesson with a phenomenal hook. I pose the following question: would you rather be given $500 a day for the month of March (usually this is when the lesson is taught) or would you rather have $.01 on March 1st, $.02 on March 2nd, $.04 on March 3rd, etc.? In the second situation, the money will double each day until reaching March 31st. Students will immediately gravitate toward the first situation: earning $500/day. But then I request proof. I ask them to grab their pencil, pick up their calculator, and start calculating how much money each scenario would give them. Earning $500 a day for the month would accrue $15,500. The second situation that begins with a penny doubling in value will give them over $10 million! They are always stunned when this happens! This purpose of this hook is to show them the power of exponential growth and how to easily build a geometric (exponential) equation. I would not change this lesson at all!
