Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population. They'll also informally prove that vampires can't be real.
How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.
How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.
How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.