Chapter 1.1, Problem 113AYU

Poverty Threshold Poverty thresholds arc determined by the U.S. Census Bureau. A poverty threshold represents the minimum annual household income for a family not to be considered poor. In 2005, the poverty threshold for a family of four with two children under the age of 18 years was $\$19,350$. In 2015, the poverty threshold for a family of four with two children under the age of 18 years was $\$24,250$. Assuming poverty thresholds increase in a straight-line fashion, use the midpoint formula to estimate the poverty threshold of a family of four with two children under the age of 18 in 2010. How does your result compare to the actual poverty threshold in 2010 of $\$22,050$?

Source: U.S Census Bureau

To determine

To find: The poverty threshold of a family of four, with two children under the age of 18, in 2010.

Answer to Problem 113AYU

The poverty threshold of a family of four with two children under the age of 18 in 2010 $=\$21800$.

Explanation of Solution

Given:

Poverty threshold of a family of four with two children under the age of 18, in 2005 was $\$19350$.

Poverty threshold of a family of four with two children under the age of 18, in 2015 was $\$24250$.

Formula used:

Midpoint formula:

$\text{M }=\left(x,y\right) = \left(\frac{\left(x_1+x_2\right)}{2}, \frac{\left(y_1+y_2\right)}{2}\right)$

Calculation:

Let the coordinates be $\left(x,y\right)=\left(\text{year, poverty threshold}\right)$.

Let the coordinates of $(x₁,y₁)=\left(2005,19350\right)$ and coordinates of $(x₂,y₂)=\left(2015,24250\right)$.

Midpoint of the above points $=\text{ M }=\left(x,y\right)=\left(\frac{2005+2015}{2}, \frac{19350+24250}{2}\right)$.

$=\left(\frac{4020}{2}, \frac{43600}{2}\right)$

$=\left(2010,21800\right)$

Poverty threshold of a family of four with two children under the age of 18, in 2010 $=\$21800$.

Actual poverty threshold value in 2010 $=\$22050$.

The calculated value is less than the actual value by $\$250$.