Question

the data in the table below shows the number of single fathers heading households with children under 18 years of age.

year
number of single u.s. fathers heading households with children younger
than 18 (millions)
1981
0.7
1991
1.4
2001
2.1
2011
2.8
a. which of the following is the correct scatter plot for the data?
a.
b.
c.
d.
b. determine the type of function the scatter plot models.
a linear function
a logarithmic function
an exponential function

Explanation:

Step1: Analyze the data trend

Looking at the values \(0.7\) (1981), \(1.4\) (1991), \(2.1\) (2001), \(2.8\) (2011). The difference between consecutive values: \(1.4 - 0.7=0.7\), \(2.1 - 1.4 = 0.7\), \(2.8 - 2.1=0.7\).

Step2: Determine the function type

Since the data has a constant difference (\(0.7\)) between consecutive \(y -\) values (where \(y\) is the number of fathers in millions) for a constant difference in \(x -\) values (where \(x\) represents the years with a 10 - year interval), it follows a linear relationship. A linear function has the form \(y=mx + b\), where \(m\) is the slope (rate of change). Here \(m = 0.7\) (per 10 - year increase).

Answer:

a. B; b. A linear function.