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Population growth reaches an upper limit in the future, at line K. When to Use this Model Use this model in locales that previously experienced high growth rates and are currently experiencing growth at a slower pace. The equation for the modified exponential model is shown in Equation An easy but imprecise way to find K is to plot census takings on graph paper and select a point where the population levels off.

An example of the modified exponential curve is provided below. The example is based on the data in Figure The upper limit for K is set at 8, residents. It is assumed that population growth is slow as a result of declining economic opportunities in the locale. Application of Equation Modified Exponential Equation To accept this projection, it is necessary to study the economy of the area as well as the carrying capacity of the land to determine if the estimate is too low or high.

For rural districts, in particular, out-migration can have a major impact on population size. Determine why growth is slow. Do young adults leave as soon as they obtain an education? Examine development plans for the district. Will new proposed activities have an impact on population growth?

Extrapolation Summary It is important to identify the projection tool that fits the available information and provides the most reasonable projection of the future. It is a difficult task that requires investigating various tools as well as the economic and demographic behavior of the locale. The following suggestions can aid in the selection and application of appropriate tools.

Plot projection results on a graph and then determine if the plot best fits the observed data. Use a different method that fits the assumptions of the data and perform another projection. Do strong differences exist? If so, determine why. Is it the data used or the tools employed? Were there enough census takings? Was a good start date selected for the first census period? Check the basic assumptions of each method employed. Do the data support the assumptions? Examine the social, economic, and demographic trends that are taking place.

Will the trends continue in the future? Do they support the projection? Both methods rely on the projection of a larger or parent population to project the population size of a sub-area. The Ratio Method The ratio method projects population growth for a sub-area using population projections for a larger or parent population.

A regional projection can be used to project the population size of districts, and a projection for the country can be used to project the population size of a region. Assumption Local population change is highly dependent on what happens to the population in the surrounding regions or states.

The ratio method can be used to project population growth for the local area if two conditions are met: similar population patterns exist for both the locale and the parent population; and it is expected to continue in the future.

The ratio method also assumes that a projection exists for the larger or parent population. As indicated in Lesson 5, projections for large areas such as a country, province, or region tend to be more reliable than those produced for smaller locales.

The ratio method summary equation is shown in Equation Equation The Ratio Method Summary Equation How to Use this Tool: Use historic census data to graph the sub-area population and the parent or state population to see if similar growth is taking place.

Collect projections for the parent population. Examine differences in the projections and determine why the differences exist.

What methods were used and what were the assumptions? The following example projects the total population of a region using the projection for a country.

A projection of a state or province could also be used as the basis to project the size of a district.

Once district projections are available, it is possible to project the size of a small town or village, provided that growth patterns are similar. An example of the ratio method follows using a projection for Ghana in year to project the population size of the Volta Region. Ideally, a projection produced by the Ghana Statistical Service would be used.

However, Ghana has only recently released their year census results, hence projections for the year were not available. Projections produced by other international organizations such as the World Bank could have also have been used.

Figures and display population trends for the region and the country. Will the Volta Region continue to have similar patterns of growth? You will have to make a judgment when using this tool.

In this case, the patterns of growth are similar but not identical. Step 2: Next, obtain a reliable projection for the larger population, in this case, Ghana. The projected size of the country for year is 22,, An application of the ratio method summary equation is shown below. Application of the Ratio Method Equation, Equation The ratio tool has a number of advantages over extrapolation techniques.

Computation is fast; it only takes a few minutes once the data and a reliable projection are available. Revisions are simple, and the ratio tool can be used to make long-range projections. There are, however, some disadvantages. First, like extrapolation tools, the ratio tool does not support the study of changes in births, deaths, and migration.

In addition, it requires a reliable projection for the larger area. Finally, it is highly dependent on the assumed relationship between the sub-area and the larger or parent population. The ratio technique is based on a single point in time when the calculation is performed. Calculate the ratio method for several points in time using the information for the parent and sub-area population.

Once these calculations have been performed, graph the ratios and use an extrapolation tool to fit the points to a curve. This approach allows the use of more census information to determine future growth. It also allows for observation of expected population growth trends graphically. It is possible to apply an adjustment factor to make sure that the projection represents its share of the projected growth of the region or parent population.

When a number of projections are performed for a region, the sum of all sub-area projections can be much higher than the projection for the parent projection. The adjustment factor, as shown in Equation brings all of the projections back to the projection of the parent population.

Equation The Adjustment Factor Steps for Using the Adjustment Factor Apply the ratio method for all sub-areas within the boundaries of the parent population. For example, use the ratio method for all regions if the parent population is the country, or for all districts if the parent population is a province, state, or other type of political boundary.

Find the proportion of the projected sub-area of the parent population. Sum all of the proportions of all sub-areas Divide the sum of the proportions by 1. Once the adjustment factor has been calculated, multiply it by the initial projection of the sub-areas.

The following example demonstrates how to develop and apply an adjustment factor. This example uses a regional projection to project the total population size of districts.

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