First post!

Hello! Welcome to STEM STUFF! Here we'll explore basically just about anything that's interesting and has to do with science, technology engineering, or mathematics. So why not jump right into it? Recently I came across something interesting in math class. (For those who don't think anything in math class could possibly be interesting, this isn't the place for you.) In our exponential function notes, there was a seemingly harmless problem: Find the intersection of an exponential function and a linear function:

graphed with https://www.desmos.com/calculator

There was a story to go along with this. The population of a country is initially 2 million people and increasing at 4% per year (the exponential function). On the other hand, the food supply of the country can initially feed 4 million people, and it can feed an additional 0.5 million people every year (the linear function). The problem asks you to find out when the country will begin to experience a food shortage (same thing as the point of intersection). So, you have two functions: y = 2(1.04)^x for the population and y = 4 + 0.5x for the food supply. To find the intersection, simply equate the right side of both equations: 4 + 0.5x = 2(1.04)^x. Solve for x, then plug it in to one of the equations to get the y value. But there's a problem, since there is an x in the exponent as well as on the "ground". This makes solving for x not so easy. I tried doing all kinds of algebra with this, including logarithms, but to no prevail. After some Googling, I learned that this is not possible to solve algebraically. This was mind-boggling to me, since I had always assumed that you could "solve for x" in an equation no matter what. The reason this is not solvable is because there is not way to combine the two x's together. There will always be one x on the "ground" and one in the exponent, or always one in a log and one outside of a log. Unable to solve algebraically, there are two options left to find the intersection point: Guess and check, or graph the equations. Unfortunately, these two methods are horribly uninteresting I try to avoid guessing and checking at all costs (plus it's more time consuming), so the best way to solve this accurately is to put the equations in a graphing calculator and tell it to calculate the point of intersection. Instantly, we can find out that the two functions intersect at approximately (78.3, 43.2). This means the country will first experience a food shortage after about 78.3 years, once it has reached a population of 43.2 million people. Although not the most interesting solution, we've just predicted a country's food shortage. Maybe graphing calculators are the answer to world hunger!

To conclude, I want to say that I know a lot of people have no idea what I was talking about here, unless you remember all your high school math classes. In the future, expect posts that involve topics that a wider audience can actually understand (still probably not all of them), and include more interesting content, hopefully. I look forward to the next few months of STEM STUFF. See you next week!