Cover Letter
In the “Small World, Isn’t It?” Project, the essential question was to find out how long until everyone is “squashed up” against one another. The number for when everyone would be squashed up against one another was 1.6 times 1015. We had one main assignment, two helping assignments, and an Honors Assignment that I had to complete for this project. The assignments are “Return to Small World Isn’t It?”, “Beginning Portfolios”, “Tweaking the Function”, and the Honors Assignment “The Limit of Their Generosity”.
In the “Beginning Portfolios” assignment, we focused on two different types of functions that we studied during this project, Linear Functions ( f(x)=mx+b ) and Exponential Functions ( f(x)=k*ecx ). We compared the two functions by looking at how each function represents rates of growth/change, how they represent starting points or initial values, and what kinds of situations are appropriate for these functions. In the “Tweaking the Function” assignment, we looked at what makes the graph of an exponential function more curvy and less curvy and what changes the horizontal and vertical positions of the graph. In the Honors Assignment, “The Limit of Their Generosity”, we looked at how natural logs (e) are used in compound interest and how changing x, or the time affects the graph.
The main assignment was “Return to Small World, Isn’t It?”. For this assignment, we were given a data chart which had the estimated population from 1650 to 2010 and the years since 1650. I used the “Beginning Portfolios” Assignment in order to help me find a function for “Return to Small World” and “Tweaking the Function” in order to help me improve it so that it was more accurate.
Personal Growth
I feel that I learned a lot more about exponential functions and how to convert graphs or data points into an exponential function. I feel that my group didn't really work together a lot because I feel that no one needed help working on this assignment. However, when someone would need help understanding the problem or what they did wrong, we would all try and help them understand it. I also feel that my ability to work well in groups has not changed.
In the “Beginning Portfolios” assignment, we focused on two different types of functions that we studied during this project, Linear Functions ( f(x)=mx+b ) and Exponential Functions ( f(x)=k*ecx ). We compared the two functions by looking at how each function represents rates of growth/change, how they represent starting points or initial values, and what kinds of situations are appropriate for these functions. In the “Tweaking the Function” assignment, we looked at what makes the graph of an exponential function more curvy and less curvy and what changes the horizontal and vertical positions of the graph. In the Honors Assignment, “The Limit of Their Generosity”, we looked at how natural logs (e) are used in compound interest and how changing x, or the time affects the graph.
The main assignment was “Return to Small World, Isn’t It?”. For this assignment, we were given a data chart which had the estimated population from 1650 to 2010 and the years since 1650. I used the “Beginning Portfolios” Assignment in order to help me find a function for “Return to Small World” and “Tweaking the Function” in order to help me improve it so that it was more accurate.
Personal Growth
I feel that I learned a lot more about exponential functions and how to convert graphs or data points into an exponential function. I feel that my group didn't really work together a lot because I feel that no one needed help working on this assignment. However, when someone would need help understanding the problem or what they did wrong, we would all try and help them understand it. I also feel that my ability to work well in groups has not changed.