Question

the table lists how poverty level income cutoffs (in dollars) for a family of four have changed over time. use the midpoint formula to approximate the poverty level cutoff in 1987 to the nearest dollar. the poverty level cutoff in 1987 was dollars. (round to the nearest dollar as needed.)

Explanation:

Step1: Identify the two years around 1987

The years around 1987 are 1980 and 1990.

Step2: Use the mid - point formula

The mid - point formula for a linear approximation between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(y=y_1+\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)\). Here \(x_1 = 1980,y_1=8716,x_2 = 1990,y_2 = 13105,x = 1987\).
First, calculate the slope \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{13105 - 8716}{1990 - 1980}=\frac{4389}{10}=438.9\).
Then, \(y=8716+438.9\times(1987 - 1980)\).
\(y=8716+438.9\times7\).
\(y=8716 + 3072.3\).

Answer:

\(11788\)