Final answer:
The linear equation expressing the population of a small town in central Florida from 2004-2015 is y = 99x - 186,800. The predicted population in 2020, if the linear decline continues, would be 225,800.
Step-by-step explanation:
In this case, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we need to determine the rate of decline in population per year. Given that the town's population doubles every 10 years, we can calculate the slope as follows:
slope = (final population - initial population) / (final year - initial year) = (100,000 - 100) / (2000 - 1900) = 9900 / 100 = 99
Now, we have the slope. To find the y-intercept, we can use one of the data points. Let's use the initial year and population:
y = mx + b
100 = 99(1900) + b
b = 100 - 99(1900) = -186,800
Therefore, the linear equation expressing the population of the small town from 2004-2015 is y = 99x - 186,800, where y represents the population and x represents the year. To predict the population in 2020, substitute x = 2020 into the equation:
y = 99(2020) - 186,800 = 225,800
Therefore, the predicted population in 2020 would be 225,800 if the linear decline continues.