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In 1984, the median family income was $26 433. In 1989, the median family income was $34 213. a) Determine the annual rate at which the median income is increasing. b) Determine the equation for the median family income given a particular year. c) Use the equation to predict the median family income in 2010.​

User SupaMario
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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.

User Pietro Coelho
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