Chapter 4, Problem 47RE

(a)

To determine

To graph: The scatter diagram of the given data.

Explanation of Solution

Given information:

The data is given percentage of persons in the United States whose income is below the poverty line..

Graph:

  

Figure 1.

Interpretation:

The graph represents the percentage of persons in the United States whose income is below the poverty line. The graph is drawn using graphing utility. The x -axis represents the percent below poverty level say p whereas y -axis is the time say t .

The scatter represent the cubic relation that appears to exist between the two variables.

(b)

To determine

The function of bets fit to the data. Also, predict the percentage of persons that were below the poverty level in 2010 with time 21.

Answer to Problem 47RE

The function is $f(x)=0.0035x^3-0.0994x^2+0.52x+13.45$ .

At time 21 the percentage of poverty level is $12.95$ .

Explanation of Solution

Given:

The given data.

Concept Used:

Use of Maple software.

Calculation:

The function of best fit to these data is cubic.

  $f(x)=0.0035x^3-0.0994x^2+0.52x+13.45$

Now,

  $f(21)=0.0035{(21)}^3-0.0994{(21)}^2+0.52(21)+13.45$

  $=12.95$

Conclusion:

The function is $f(x)=0.0035x^3-0.0994x^2+0.52x+13.45$ .

At time 21 the percentage of poverty level is $12.95$ .

(c)

To determine

To graph: The scatter diagram with the function of the given data.

Explanation of Solution

Given information:

The data is given percentage of persons in the United States whose income is below the poverty line.

Graph:

  

Figure 2.

Interpretation:

The graph represents the percentage of persons in the United States whose income is below the poverty line. The relation between the scatters are cubic. Hence, the curve is the function that fits the data . The graph is drawn using graphing utility. The x -axis represents the percent below poverty level say p whereas y -axis is the time say t .