Q. 113 - Precalculus Enhanced with Graphing Utilities

Question

Poverty Threshold Poverty thresholds are 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 2001, the poverty threshold for a family of four with two children under the age of 18 years was \(17,960. In 2011, the poverty threshold for a family of four with two children under the age of 18 years was \)22,350. 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 2006. How does your result compare to the actual poverty threshold in 2006 of $20,444?

Step-by-Step Solution

Answer

Our result $\left(2006,20020\right)$ is a bit lower than actual poverty threshold. 

Step 1. Given Information

In 2001, the poverty threshold for a family of four with two children under the age of

18 years was $17,960. In 2011, the poverty threshold for a family of four with two children under the age of 18 years was $22,350.

We have to compare result to the actual poverty threshold in 2006 of $20,444?

Step 2. Identifying coordinates

In 2001, poverty threshold was $17,960 and in 2011, poverty threshold was $22,350.

The two points are $\left(2001,17960\right) and \left(2011,22350\right)$

Step 3. Finding poverty threshold

$\left(\frac{2001+2011}{2},\frac{17960+22350}{2}\right)=\left(2006,20020\right)$