Population Movement

In 2000, a country's population, broken down by regions, was:
- Northeast: 53.6 million
- Midwest: 64.4 million
- South: 100.2 million
- West: 63.2 million

In 2010, the population was:
- Northeast: 57.3 million
- Midwest: 70.9 million
- South: 114.6 million
- West: 64.9 million

Tasks:

1. Set up the population figures for each year as a row vector.

- Population in 2000 (in millions): [53.6, 64.4, 100.2, 63.2]
- Population in 2010 (in millions): [57.3, 70.9, 114.6, 64.9]

2. Use matrix operations to find the net increase or decrease of population in each region from 2000 to 2010.

- Population Net Change (in millions):
- Northeast: 57.3 - 53.6
- Midwest: 70.9 - 64.4
- South: 114.6 - 100.2
- West: 64.9 - 63.2

3. Assuming the same population growth from 2010 to 2020 as from 2000 to 2010, use matrix operations to predict the population in each region in 2020.

- Predicted Population in 2020 (in millions):
- Northeast: 57.3 + (57.3 - 53.6)
- Midwest: 70.9 + (70.9 - 64.4)
- South: 114.6 + (114.6 - 100.2)
- West: 64.9 + (64.9 - 63.2)

To find the net increase or decrease of population in each region from 2000 to 2010, subtract the population in 2000 from the population in 2010 for each region. Assuming the same population growth from 2010 to 2020 as from 2000 to 2010, predict the population in each region in 2020 by adding the net change in population from 2000 to 2010 to the population in 2010 for each region.

Explanation:

To find the net increase or decrease of population in each region from 2000 to 2010, we need to subtract the population in 2000 from the population in 2010 for each region. We can do this using matrix operations. The net population change in each region can be calculated by subtracting the population in 2000 from the population in 2010. Using matrix subtraction, we subtract the population matrix in 2000 from the population matrix in 2010, element by element. The resulting matrix will give us the net change in population for each region.

Northeast Midwest South West
Population Net Change (in millions)
57.3 - 53.6 = 3.7 70.9 - 64.4 = 6.5 114.6 - 100.2 = 14.4 64.9 - 63.2 = 1.7

Assuming the same population growth from 2010 to 2020 as from 2000 to 2010, we can predict the population in each region in 2020. To do this, we need to add the net change in population from 2000 to 2010 to the population in 2010 for each region. Using matrix addition, we add the net change matrix to the population matrix in 2010, element by element. The resulting matrix will give us the predicted population for each region in 2020.

Northeast Midwest South West
Population in 2020 (in millions)
57.3 + 3.7 = 61 70.9 + 6.5 = 77.4 114.6 + 14.4 = 129 64.9 + 1.7 = 66.6

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