The town of Appleville recorded the following dates and populations.
YEAR POPULATION
(in thousands)
1980 51.5
1985 53
1990 56
1995 62
Estimate the approximate population of Appleville in 1988 by finding an equation and then substituting.
To estimate the approximate population of Appleville in 1988, we can use a linear equation based on the given data points.
Let's assume that the population follows a linear trend over time. We can use the data points from 1980 (51.5 thousand) and 1990 (56 thousand) to find the equation of a line.
First, let's determine the rate of change (slope) of the population over 10 years:
Change in population = 56 - 51.5 = 4.5
Change in years = 1990 - 1980 = 10
Slope = Change in population / Change in years = 4.5 / 10 = 0.45
Now, we can use the slope-intercept form of a linear equation:
y = mx + b
Where:
y = population
x = year
m = slope
b = y-intercept
Since the population in 1980 (x = 0) is given as 51.5, we can find the y-intercept:
51.5 = 0.45(0) + b
51.5 = b
So the equation for the population over time is:
y = 0.45x + 51.5
Now, we can substitute the value of x = 1988 into the equation to estimate the approximate population in 1988:
y = 0.45(1988) + 51.5
y ā 893.6 thousand
Therefore, the approximate population of Appleville in 1988 is estimated to be around 893.6 thousand.