r = (Pt2/Pt1 – 1)

r = (Pt2/Pt1 – 1) X 100%

Where Pt1 is the first time period and Pt2 is the second time period. In this case, each time period represents a decennial census year, and this equation divides the later census year by the earlier one. This equation assumes that rate of change over 10 years is equally divided across those years.

Geometric projection is defined by the equation:

Pt+n = Pt (1 + r)n

Where Pt+n is the population of the year being projected to, Pt is the population of the year of which the rate of change is computed from, r is the rate of change, and n indicates the number of time periods (in this case census years) being projected forward. Geometric projection is a conservative estimate, meaning that it assumes that the population will change by a set rate between time periods and divided equally by each year, which is a quite linear estimate.

Exponential projection is defined by the equation:

Pt+n = Pt er*n

Where Pt+n, Pt, n, and r hold the same definitions as in geometric projection, and “e” is a constant derived from the base of the natural logarithm and exponential functions, with an approximate value of 2.71828. Exponential projection assumes that growth is compounded across each year, the growth rate is applied continuously, and assumes no upper limit as a result of unlimited resources and no external constraints on population growth. 

Table 3 compares both geometric and exponential projection methods for the county in 2030 and 2050 using the 2010 census population data as the base population and the 2010-2020 rate of change as the predicting variable. The geometric projection for 2030 shows a population that is around 97 thousand more than what was recorded in 2010 and 55 thousand more people than in 2020. These values are large but seem realistic based of the growth from 2010 to 2020. On the other hand, the exponential projection for 2030 was only moderately higher, calculating around 116 thousand more people compared to 2010 and around 74 thousand more people compared to 2020.  However, when projecting into 2050, the difference between geometric and exponential projections was much higher, with the exponential population calculating around 68 thousand more people. This means that when projecting far into the future, using 2010 as a base population might exacerbate the trend of higher exponential projections due to compounding growth.

Table 4 depicts the population predictions for 2030 and 2050 using the 2020 census population data as the base population and the 2010-2020 rate of change as the predicting variable. Geometric projections for 2030 and 2050 were the same as in Table 3, when 2010 was used as the base population. This reveals these numbers represent a stable lower bound in which the current Utah population could realistically grow to if it kept up its current growth. On the other hand, the exponential projections were lower than in Table 3 by a range of 10 to 20 thousand people. This suggests that when using 2020 as the base population, you get a lower and thus more realistic exponential projection as the upper bounds of the future Washington County population.

Overall Washington Couty, Utah seems that it will continue to have a growing population due to its favorable conditions. Historically, it has been a town with many booms and busts, with the exceptionally large growth and fall of silver mining, cotton and grape farming, and dam resilience. Since white settlers it has been a place for American economic experimentation, and eventually became directed by the Church of Latter-day Saints. Today, its strong Mormon Community maintains the high number of young families, while its ecotourism and famous golf courses invite increasingly more seasonal residents (Utah Historical Society 2025). Even though Utah is one of the youngest states (in terms of population age) in county, the growth projections for 2050 tell us they might need to start investing resources in a bigger aging population (Miller 2023).

U.S. Bureau of the Census. 2010 Census of Population and Housing. www.data.census.gov

U.S. Bureau of the Census. 2020 Census of Population and Housing. www.data.census.gov

Utah Historical Society. 2025. “Washington County.” I Love History. Accessed May 11, 2025. https://ilovehistory.utah.gov/washington-county/.

Cite:

U.S. Census Bureau. "TOTAL POPULATION." Decennial Census, DEC Demographic and Housing Characteristics, Table P1, 2020, https://data.census.gov/table/DECENNIALDHC2020.P1?q=population&g=050XX00US49053&y=2020&d=DEC+Demographic+and+Housing+Characteristics. Accessed on May 11, 2025.

U.S. Census Bureau. "TOTAL POPULATION." Decennial Census, DEC Summary File 1, Table P1, 2010, https://data.census.gov/table/DECENNIALSF12010.P1?q=population&g=050XX00US49053&y=2010&d=DEC+Summary+File+1. Accessed on May 11, 2025.

U.S. Census Bureau. "URBAN AND RURAL." Decennial Census, DEC Summary File 1, Table P2, 2010, https://data.census.gov/table/DECENNIALSF12010.P2?q=URBAN+AND+RURAL&g=050XX00US49053&y=2010. Accessed on May 11, 2025.

U.S. Census Bureau. "URBAN AND RURAL." Decennial Census, DEC Demographic and Housing Characteristics, Table P2, 2020, https://data.census.gov/table/DECENNIALDHC2020.P2?q=URBAN+AND+RURAL&g=050XX00US49053&y=2020. Accessed on May 11, 2025.

https://www.amatravel.ca/articles/why-utah-is-a-great-snowbird-destination

https://shorelight.com/universities/undergraduate/utah-tech-university/

https://www.sltrib.com/news/education/2023/01/30/name-dixie-lives-st-george/#:~:text=Dixie%20State%20University's%20name%20became,the%20Confederacy%20and%20white%20supremacy.

https://www.vrbo.com/vacation-rentals/usa/utah/washington-county

Youth Dependency = 100 * (Youth Population/Working Population)

Aged Dependency = 100 * (Aged Population/Working Population)

The Total dependency ratio was calculated by using a similar formula:

Total Dependency = 100 * ((Aged Population+Youth Population)/Working Population)

= Youth Dependency + Aged Dependency

I calculated the percentage of the total population each broad racial and specific ethnic or national origin represented in both census years using the formula Population of Subgroup/Total Population*100, the subgroups in this case being the various racial categories and ethnicities recognized by the census and the total population being that of Washington County, Utah. I then calculated the percent change for each ethnic subgroup between 2010 and 2020 using the formula [(Population in 2020/Population in 2010)-1]*100.

I am not aware of any weaknesses in the data or these formulas.

A population as small as Washington County, Utah is a good example of how raw numbers affect percent change and can make the latter very large when describing small numbers of people. For instance, the Indonesian population grew by a whopping 750% between 2010 and 2020—but that’s because there were only eight Indonesians resident in the county in 2010, and there were 68 in 2020. Neither number is significant, accounting for just 0.01% of the total population in 2010 and 0.04% in 2020. It is notable that every broad racial category and every subcategory had a positive percent change above 17%; Washington County, Utah is growing in absolute numbers in every racial and ethnic category, a fact that is reflected in the percent change column in Table 6.

The formula for the Index of Dissimilarity is: D= 0.5 S| P_ig/P_g-P_ih/P_h|. First, the total of each subgroup was found ie. White. Then, we computed what proportion of that total resides in that census tract ie. Whites in tract 1/ Total white population for that census year and borough. After, the absolute values of the difference of W/B, W/A, and B/A were found. Finally, the values of those two groups i.e W/B were added and then multiplied by 0.5, where 0.5 odds that a person is of one group or another. One of the limitations per say that this formula carries is that it only compares two groups at a time. We're not able to compare multiple different racial groups at the same time. Since it focuses on just one racial or ethnic pair at a time, it can miss broader patterns of segregation and overlook more complex group dynamics. In highly diverse places like California, New York City or Miami, the Dissimilarity Index may not be the most effective tool for understanding segregation. In this case, Washington county, Utah, is a relatively small geographical area, with a smaller population, so this index is of better use.

https://greaterzion.com/

I will be using the Census Bureau population and housing data from 2010 and 2020. The racial groups are broad racial categories of Hispanic, Asian, and other mixed races. The goal is to compare the racial diversity in Washington County.

In this case the result is r=0.305 or 30.5%