Look at the following example: Which picture has four apples? A B C D B is the expected answer but should not the correct answer be BCD? Technically if a set has exactly $m$ elements, then it has $k$ elements if $k\leq m$. This is also how we talk in everyday language: "Do you have three doll...

So I'm wrapping up my second year teaching high school calculus, and my first as an AP course. In addition to review, I'd like to end the year by giving the students a taste of the kinds of real-world applications that they can now start to appreciate now that they have a conceptual understandin...