Answer:
Explanation:
a) To determine the annual rate at which the median income is increasing, we can use the formula:
annual growth rate = (final value / initial value) ^ (1 / number of years) - 1
Using 1984 as the initial year and 1989 as the final year, we get:
annual growth rate = ($34,213 / $26,433) ^ (1 / 5) - 1
annual growth rate ≈ 5.05%
Therefore, the median family income is increasing at an annual rate of approximately 5.05%.
b) To determine the equation for the median family income given a particular year, we can use the slope-intercept form of a linear equation:
y = mx + b
where y is the dependent variable (median family income), x is the independent variable (year), m is the slope (annual growth rate), and b is the y-intercept (median family income in the initial year).
Using the values from 1984 and 1989, we can find the values of m and b:
m = 0.0505
b = $26,433
Therefore, the equation for the median family income is:
y = 0.0505x + $26,433
c) Using the equation y = 0.0505x + $26,433, we can predict the median family income in 2010 by substituting x = 26 (since 2010 is 26 years after 1984):
y = 0.0505(26) + $26,433
y ≈ $39,360
Therefore, we can predict that the median family income in 2010 was approximately $39,360.