Reflection:
This problem is designed for students in upper high school grades or college level work. It uses concepts from calculus and algebra, interweaving these concepts into a multi-step problem. Students are required to use problem solving skills to arrive at the correct answer and make inferences about the problem. Problem solving in math is not just about applying formulas. It is about applying ideas to a problem and using formulas in different ways. It is about thinking about where you want to end up, and thinking of a plan to get to the final destination. When problem solving, many times you end up with a surprising solution. This problem requires students to think outside of the box to arrive at a numerical answer in a problem where they are not given any numbers.