A man stopped me in the supermarket, confused by a sign below the napkins. It advertised two containers of napkins for $5 or $4. He wanted to know which was the real price. Upon reading the print that was perhaps too small for his eyes, I discovered "after mail-in rebate" printed below the $4. Even if he invites a deluge of junk mail by filling out their form (assuming there is one), will he see that dollar? Unlikely. I've never received a mail-in rebate without first complaining to the Better Business Bureau. How can we discourage this common scam? The answer can be found in any calculus textbook.
Up to 50 rebate cards are mailed to the company, one from every state in which the rebate is offered. At the end of the 6-8 weeks or whatever timeframe the company advertises, we compute the number, n, of states where a rebate has not arrived. The company is then fined e^n times the value of the rebate, rounded to the nearest penny. Accidentally lose one form? Don't worry, that's only $2.78. 10 rebate requests go unanswered? That's sounding a little less accidental. Fork over the $22,026.47. Screw over one person from every state in America? Well, your corporation probably can't afford the $5,184,705,528,587,072,464,087.45, but you can declare bankruptcy and let honest people take your place. Not only does this proposal fight fraud and help consumers, it will help teach children about exponential growth and one of the most fundamental constants in mathematics. And wouldn't it be cool to have the limit as n tends to infinity of (1+1/n)^n in the US Code?