Math in the Real World
Problem 1: From the growth and decay of bacteria to the population of squirrels in your neighbor's backyard, functions can model all sorts of things. But what about when you want to know what happens a long time from now? How many squirrels can that giant oak tree really hold before the squirrels start looking elsewhere? How do we get there? While we don't have all the answers, we know limits can help. First, we need to know or be refreshed about one our favorite equations: the equation for logistic growth. We like it for what it can do, not necessarily how it looks. All those letters stand for: y = the population of whatever we might be analyzing L = the carrying capacity k = a constant t = time Okay, we admit that's a lot to take in and a little bit confusing to boot. Let's give you some context to help things along. Suppose we had a population of Emperor Penguins in Antarctica, which we learn, after c...