Exponential Growth Project

In the popular movie and book, Pay it Forward, a student is challenged by his teacher to find a way to change the world. The student decides to help three people in need, and after doing so tells each of those three people to help three more people in need, and so on. Hence the saying "Pay it Forward". Let's take this idea and roll with it, and explore the mathematics behind this process.

Using the above scenario as the guiding prompt for the project, you will first create a Tree Diagram that models this scenario for four rounds. This can be done by hand or using online webtools.

Then, using any table generating program, create a table of values that shows the number of people helped per round for six rounds. From your created table, derive the equation that models the results.

Using Desmos, construct a graph of the derived equation and save the graph as a PDF.

You will produce a report that includes the tree diagram, table, derived equation, and graph, as well as a brief 2-3 paragraph analysis which will include the following:

• Connection of the results to that of linear growth and exponential growth and state which of the two is being represented by this scenario and why it's the better fit.
• State a prediction based off the equation and/or graph for how many people will have been helped after 10 rounds. Is this surprising?
• Interpret the existence of y-intercepts and x-intercepts of the graph. If they exist, state what they are. If they do not exist, explain why.