Formulas applied to the 2000, 2010, and 2020 decennial population totals are as follows:

Rate of change: r= (P_t2/P_t1-1)

Geometric Projections: P_t+n = P_t(1+r)ⁿ

Exponential Projections: P_t+n = P_t e^r*n

Geometric and exponential projections utilize previous rates of change to anticipate future progressions in growth. Generally, the geometric is a more conservative projection than exponential. Our formulas carry two notable assumptions. First, growth is assumed to be equally divided across every ten years. And second, all four formulas assume the projected population will follow the same rate of growth over time.

Results

In slower-growing areas, the difference between the two projections is minimal. In the case of Orange County, VT, this is certainly the case - a result of its being a county that experienced minimal growth between the 2000-2020 decades. Interestingly, we see relatively lowered geometric and exponential projections for 2050. That is, they are lower than those projected for 2030. This is explained by a 2020 rate of change which is half that of 2010. With total population rates of change sitting at 2.5 percent in 2010, but 1.1 percent in 2020. This explains the apparent discrepancy.

Youth Dependency Ratio (YDR)

YDR = Population(0-14)/Population(15-64) x 100

Aged Dependency Ratio (ADR)

ADR = Population(65+)/Population(15-64) x 100

Total Dependency Ratio (TDR)

TDR = Population(0-14) + Population(65+)/Population(15-64) x 100

Results

From Table 4, it can be seen that in 2010, Orange County in Vermont had more children than senior citizens. This is because the Youth Dependency Ratio was greater than the Aged Dependency Ratio. As a result, this shows that families in Orange County, Vermont tend to have more children. However, in 2020, Orange County in Vermont had a higher Aged Dependency Ratio than Youth Dependency Ratio which is evident that there are many more senior citizens in that county than children. Youth and senior citizens depend on the workforce, with an age cohort of 15-64. This statement is also just an assumption on the workforce since there are senior citizens over the age of 64 who are still working, as well as, youths under the age of 15 who are working too. The Total Dependency Ratio for Orange County, Vermont in 2010 was 46.187 which shows that a little less than half the total county population depends on the working class. However, in 2020, the Total Dependency Ratio was 56.51 which shows that a little more than half the county population depended on the working class. In conclusion, Dependency Ratios can tell us how a population looks demographically.

Methodology:

The Index of Dissimilarity (D) was calculated using the formula:

D = 0.5 Σ |P_ig / P_g - P_ih / P_h|

Where:

• P_ig​: Population of group g in census tract i

• P_ih​: Population of group h in census tract i

• P_g​: Total population of group g across all census tracts

• P_h​: Total population of group h across all census tracts

Results:

The results show different trends in the distribution of racial groups in Orange County, Vermont, between 2010 and 2020. Whites and Blacks became more evenly spread, with the Index of Dissimilarity (D) decreasing from 0.224 in 2010 to 0.176 in 2020, indicating improved integration between these groups. In contrast, Whites and Asians became slightly more separated, as D increased from 0.241 to 0.263, suggesting a need to explore factors contributing to this change. For Blacks and Asians, the D value decreased slightly from 0.260 to 0.246, reflecting modest progress toward greater mixing. Overall, these results highlight progress in integration between some groups, such as Whites and Blacks, while also pointing to areas, like Whites and Asians, where segregation has increased. These findings emphasize the importance of understanding demographic shifts and encouraging balanced communities.

Table 1 shows the total population and rate of change in Orange County, Vermont. The total population was calculated by adding the sum of all racial categories. The formula I used to calculate the Total Population is the following, Total Population = ∑ⁿ _I=0 P_i where P_i is the population of the i-nth racial group and n is the number of racial groups.

The formula that I used to calculate the rate of change is the following, rate of change = (P_t2/P_t1 – 1), where P_t2 is the population of time period 2 and P_t1 is the population of time period 1.

Conclusion

From Table 1, the population of Orange County, VT has a slight increase from 28,936 to 29,277. The biggest racial population in 2010 was whites, nearly dominating the entire county with a population of 28,077. But as shown, the white population has decreased from 2010 to 2020 by slightly but still the most dominate racial group in Orange County, VT. The rate of change during this 10 year time period for whites was -0.0391 as noted by the slight decline in their population. Most other demographics have a positive increase in population naming a few: Black or African alone, American Indian/Alaska Native, and Asian alone. Though there is an positive rate of change in these racial categories, whites still remain to be the majority in Orange County, VT from 2010 to 2020.

The Ethnic Index can be calculated in two ways: the normalized/standardized and unnormalized/unstandardized Ethnic Index. We calculated the normalized/standardized Ethnic Index since the unnormalized/unstandardized version is more difficult to interpret.

The two-step formula to calculate the normalized Ethnic Index is as follows:

- Σ [ (P_k/P) * ln (P_k/P) ]
      k=1

H* = H/ln n (normalized)

n = the total number of subgroups present in the population

P_k = the population of the k^th subgroup

P = the total population of all subgroups included in the index

Results:

Table 8 displays the Ethnic Entropy of Orange County, VT. The Ethnic Entropy of an area is a value from 0 to 1 where 0 represents the dominance of one ethnicity or race and 1 represents the highest amount of equality in ethnic or racial representation. It can be seen that in the Broad Racial Categories, there is a very low Ethnic Entropy value of 0.054 in 2010 and 0.082 in 2020. This means that the population of Orange County, VT is heavily dominated by one ethnicity. It can also be seen that the Hispanic or Latino populations in Orange County, VT have the highest Ethnic Entropy of 0.852 in 2010 and 0.92- in 2020. These values are very close to 1 meaning that the ethnic representation of Hispanic or Latino populations is very evenly distributed. The Asian populations are also quite equally represented. The Ethnic Entropy of 0.817 in 2010 and 0.734 for Asian populations is not as high as the Hispanic or Latino values, but they are still high nonetheless. Overall, Orange County, VT has a population that is heavily dominated by one ethnicity or race, but the Hispanic or Latino and Asian populations specifically have a high level of equal ethnic representation among themselves.

The data presented in Table 6 were obtained and analyzed to understand the changes in the ethnic and racial composition of Orange County, Vermont, between 2010 and 2020. I aggregated data from the U.S. Census Bureau and the American Community Survey (ACS), ensuring consistency in geographic scope and methodology across time periods.

To calculate the total population for each year, I summed all racial and ethnic subgroups. The absolute change over the decade was derived by subtracting the 2010 population from the 2020 population for each subgroup. I calculated the percentage change using the formula: (P2020/P2010−1)×100(P_{2020}/P_{2010} - 1) \times 100(P2020​/P2010​−1)×100, where P2020P_{2020}P2020​ is the population in 2020 and P2010P_{2010}P2010​ is the population in 2010. These calculations allowed me to clearly identify demographic shifts over the ten-year period.

Results
The data from 2010 to 2020 reveal that Orange County, Vermont, remains predominantly White, with the White population slightly declining from 28,077 to 26,978, representing a decrease of -3.91%. The Hispanic or Latino population increased significantly, from 317 to 398, a growth of 25.55%, driven primarily by Central Americans, particularly Nicaraguans, whose numbers rose from 0 to 60. However, Mexicans experienced a notable decline (-43.45%). The Asian population decreased from 137 to 102 (-25.55%), but the Filipino subgroup grew sharply (+206.67%). The Black or African American population increased from 110 to 162 (+47.27%). Individuals of two or more races saw significant growth, rising from 439 to 1,635 (+272.44%), with notable increases in those identifying as White and Black or African American (+71.43%). Despite these changes, the county remains largely homogeneous, with a small but growing diversity.