Questions: A poverty threshold represents the minimum annual household income for a family not to be considered poor. In 1995, the poverty threshold for a family of four with two children under the age of 18 years was 15,711. In 2005, the poverty threshold for a family of four with two children under the age of 18 years was 19,215. 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 2000. The poverty threshold of a family of four with two children under the age of 18 in 2000 is

A poverty threshold represents the minimum annual household income for a family not to be considered poor. In 1995, the poverty threshold for a family of four with two children under the age of 18 years was 15,711. In 2005, the poverty threshold for a family of four with two children under the age of 18 years was 19,215. 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 2000. The poverty threshold of a family of four with two children under the age of 18 in 2000 is
Transcript text: A poverty threshold represents the minimum annual household income for a family not to be considered poor. In 1995, the poverty threshold for a family of four with two children under the age of 18 years was $\$ 15,711$. In 2005 , the poverty threshold for a family of four with two children under the age of 18 years was $\$ 19,215$. 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 2000. The poverty threshold of a family of four with two children under the age of 18 in 2000 is $\$ \square$
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Solution

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Solution Steps

To estimate the poverty threshold in 2000, we can use the midpoint formula, which is a method to find the average of two numbers. Since the poverty thresholds are assumed to increase linearly, the threshold in 2000 would be the midpoint between the thresholds in 1995 and 2005. We calculate this by averaging the two given thresholds.

Step 1: Identify the Given Values

We are given the poverty thresholds for a family of four with two children under the age of 18 in the years 1995 and 2005. Specifically, the threshold in 1995 is \( \$15,711 \) and in 2005 it is \( \$19,215 \).

Step 2: Use the Midpoint Formula

To estimate the poverty threshold in 2000, we use the midpoint formula, which calculates the average of the two given thresholds. The formula is:

\[ \text{Midpoint} = \frac{\text{Threshold}_{1995} + \text{Threshold}_{2005}}{2} \]

Substituting the given values:

\[ \text{Midpoint} = \frac{15711 + 19215}{2} \]

Step 3: Calculate the Midpoint

Perform the calculation:

\[ \text{Midpoint} = \frac{34926}{2} = 17463 \]

Final Answer

The estimated poverty threshold for a family of four with two children under the age of 18 in the year 2000 is \(\boxed{\$17,463}\).

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