### Population Growth Analysis: Kuwait and BulgariaKuwait, located at the head of the Persian Gulf, has one of the greatest population growth rates in the world. Bulgaria, in southeastern Europe, has one of the smallest. Use an exponential growth/decay model to complete the table below. (Round your answers to the nearest integer.)#### Population Data:| Country | Population 2010 | Annual Growth Rate | Estimated Population 2019 ||-----------|-----------------|--------------------|---------------------------|| Kuwait | 2,789,132 | 3.501% | 3,801,631 || Bulgaria | 7,148,785 | -0.768% | 6,669,572 |### ExplanationThis table provides the 2010 population figures for Kuwait and Bulgaria, along with their respective annual growth rates. It further includes the estimated population for 2019.#### Annual Growth Rate:- **Kuwait**: 3.501% growth rate signifies a positive increase in population over the years.- **Bulgaria**: -0.768% growth rate indicates a population decline.The exponential growth/decay model formula used for estimating the future population is as follows:\[ P(t) = P_0 \times (1 + r)^t \]- $ P(t) $ is the future population.- $ P_0 $ is the initial population.- $ r $ is the annual growth rate (expressed as a decimal).- $ t $ is the time in years between the initial count and the future estimate.**Note**: The estimated populations listed (3,801,631 for Kuwait and 6,669,572 for Bulgaria) are marked with an "X", indicating the need to use the exponential model to re-calculate and verify these figures for accurate estimates.

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Kuwait, located at the head of the Persian Gulf, has one of the greatest population growth rates in the world. Bulgaria, in southeastern Europe, has one of the smallest. Use an exponential growth/decay model to complete the table. (Round your answers to the nearest integer.) Population 2010 Annual growth rate Estimated Country population 2019 Kuwait 2,789,132 3.501% 3,801,631 Bulgaria 7,148,785 -0.768% 6,669,572

Kuwait, located at the head of the Persian Gulf, has one of the greatest population growth rates in the world. Bulgaria, in southeastern Europe, has one of the smallest. Use an exponential growth/decay model to complete the table. (Round your answers to the nearest integer.) Population 2010 Annual growth rate Estimated Country population 2019 Kuwait 2,789,132 3.501% 3,801,631 Bulgaria 7,148,785 -0.768% 6,669,572

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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### Population Growth Analysis: Kuwait and Bulgaria

Kuwait, located at the head of the Persian Gulf, has one of the greatest population growth rates in the world. Bulgaria, in southeastern Europe, has one of the smallest. Use an exponential growth/decay model to complete the table below. (Round your answers to the nearest integer.)

#### Population Data:

| Country | Population 2010 | Annual Growth Rate | Estimated Population 2019 |
|-----------|-----------------|--------------------|---------------------------|
| Kuwait | 2,789,132 | 3.501% | 3,801,631 |
| Bulgaria | 7,148,785 | -0.768% | 6,669,572 |

### Explanation

This table provides the 2010 population figures for Kuwait and Bulgaria, along with their respective annual growth rates. It further includes the estimated population for 2019.

#### Annual Growth Rate:
- **Kuwait**: 3.501% growth rate signifies a positive increase in population over the years.
- **Bulgaria**: -0.768% growth rate indicates a population decline.

The exponential growth/decay model formula used for estimating the future population is as follows:

\[ P(t) = P_0 \times (1 + r)^t \]

- $ P(t) $ is the future population.
- $ P_0 $ is the initial population.
- $ r $ is the annual growth rate (expressed as a decimal).
- $ t $ is the time in years between the initial count and the future estimate.

**Note**: The estimated populations listed (3,801,631 for Kuwait and 6,669,572 for Bulgaria) are marked with an "X", indicating the need to use the exponential model to re-calculate and verify these figures for accurate estimates.

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