1. The problem is to analyze the population growth over the years given the data points: (1970, 10), (1980, 20), (1990, 40), and (2000, 50) where population is in thousands. 2. We can use the formula for the slope between two points to understand the rate of change in population: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $m$ is the slope, $y$ is population, and $x$ is year. 3. Calculate the slope between 1970 and 1980: $$m = \frac{20 - 10}{1980 - 1970} = \frac{10}{10} = 1$$ This means the population increased by 1 thousand people per year in this period. 4. Calculate the slope between 1980 and 1990: $$m = \frac{40 - 20}{1990 - 1980} = \frac{20}{10} = 2$$ Population increased by 2 thousand people per year in this period. 5. Calculate the slope between 1990 and 2000: $$m = \frac{50 - 40}{2000 - 1990} = \frac{10}{10} = 1$$ Population increased by 1 thousand people per year in this period. 6. The population growth rate changed over the decades, increasing faster between 1980 and 1990. 7. To model the population approximately, piecewise linear functions can be used for each decade segment. Final answer: The population growth rates are 1, 2, and 1 thousand people per year for the decades 1970-1980, 1980-1990, and 1990-2000 respectively.