The basis of math is around problem solving. In any application of math, the end goal is to find a solution. In teaching, professors are telling students the means necessary to "find x", "the distance", "the volume", or a plethora of other things. In the real world. people are assigned with the responsibility to find these things on a much greater scale, ranging from data analysis of a company to the architecture of a new building or bridge. It is the problem solving such as this that is able to give students the context as to why they are learning how to make these calculations. Problem solving is able to provide students with the skills needed to create different strategies for approaching a problem, whether it be in the classroom or applied to a real-world situation.
I like this exponential problem in particular, because it makes one rely on knowledge in their head and not from the calculator. We as a society cannot become complacent and believe that technology is going to solve all our problems for us. For math in particular, this problem reinforces the idea of the importance of remembering certain properties learned in mathematics. By remembering mathematical properties, it can greatly expedite the process of problem solving, making a problem that might look difficult from the outside, become simple.
I like this exponential problem in particular, because it makes one rely on knowledge in their head and not from the calculator. We as a society cannot become complacent and believe that technology is going to solve all our problems for us. For math in particular, this problem reinforces the idea of the importance of remembering certain properties learned in mathematics. By remembering mathematical properties, it can greatly expedite the process of problem solving, making a problem that might look difficult from the outside, become simple.