**The Growth Model **

The population and land area of Terratopia will be based upon the growth patterns of Las Vegas, Nevada and the surrounding suburbs in Clark County, an area in the US with one of the least amounts of urban sprawl^{[1]} despite large spikes in population—an increase of 77.3% from 1990 to 2000.^{[2]} Another reason Las Vegas was chosen is how it grew generally radially outward (as seen in the figure below), which makes the growth of Terratopia easier to quantify.

Figure 1. Satellite images showing growth of Las Vegas metro area over time.^{[3]}

Due to the fact that this rapid expansion did not come at the expense of urban sprawl, it is therefore an appropriate city to model after for Terratopia.

Terratopia’s growth in area and population was roughly modeled on the growth of Las Vegas, Nevada and the surrounding suburbs within Clark County starting in 1950. Using US Census data from Nevada^{[4]} and information from the a United States Geological survey in Nevada,^{[5]} the growth of Terratopia can be modeled with exponential functions:

P=60009(1.0679)^{t}

where P is the population of Clark County, t is in years since 1950 and

A=90380191(1.0227)^{t}

where A is the urban area of Las Vegas in meters squared and t is years since 1950.

Model City Statistics

- Same area expansion and density change patterns as Las Vegas, Nevada between the years 1950 and 2000.
- Same centerline road density (length) as 2020 Las Vegas, Nevada
- 87 miles centerline road/83 square mile
^{[6]} - 6.51×10^-4 m of centerline roadway/m
^{2} - Assume each tree takes up area of 3m
^{2}

- 87 miles centerline road/83 square mile
- Same public school to population ratio as Boston, MA
- Around 3562 population/school ratio
^{[7]} - Public schools will likely have at least one external wall of around 9 square meters and at least one segment of rooftop of around 37 square meters.

- Around 3562 population/school ratio