How To Solve Growth And Decay Problems
When it's a rate of increase, you have an exponential growth function!
Check out these kinds of exponential functions in this tutorial!
two function formulas were used to easily illustrate the concepts of growth and decay in applied situations.
If a quantity grows by a fixed percent at regular intervals, the pattern can be depicted by these functions..
For example, bacteria will continue to grow over a 24 hours period, producing new bacteria which will also grow.
In this section, we examine exponential growth and decay in the context of some of these applications. These systems follow a model of the form \(y=y_0e^,\) where \(y_0\) represents the initial state of the system and \(k\) is a positive constant, called the growth constant.Notice that after only 2 hours (120 minutes), the population is 10 times its original size!Note that we are using a continuous function to model what is inherently discrete behavior.If something increases at a constant rate, you may have exponential growth on your hands.In this tutorial, learn how to turn a word problem into an exponential growth function. Check out this tutorial where you'll see exactly what order you need to follow when you simplify expressions.No matter the particular letters used, the green variable stands for the ending amount, the blue variable stands for the beginning amount, the red variable stands for the growth or decay constant, and the purple variable stands for time.Get comfortable with this formula; you'll be seeing a lot of it.You'll also see what happens when you don't follow these rules, and you'll find out why order of operations is so important!Exponential functions often involve the rate of increase or decrease of something.Many math classes, math books, and math instructors leave off the units for the growth and decay rates.However, if you see this topic again in chemistry or physics, you will probably be expected to use proper units ("growth-decay constant / time"), as I have displayed above.