Answer:
Table C, Table D, Table E
Step-by-step explanation:
See attachment for tables
Given
[tex]p = 3.25b[/tex]
Required
Which of the tables is more expensive than the given function
To answer this question, we simply determine the equation of each table and then compare the equation with [tex]p = 3.25b[/tex]
Table A:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (1,2.75)[/tex]
[tex](b_2,p_2) = (4,11)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{11 - 2.75}{4 - 1}[/tex]
[tex]m = \frac{8.25}{3}[/tex]
[tex]m = 2.75[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 2.75 = 2.75(b-1)[/tex]
[tex]p - 2.75 = 2.75b-2.75[/tex]
[tex]p = 2.75b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]2.75 < 3.25[/tex]
Hence:
This equation is less expensive than [tex]p = 3.25b[/tex]
Table B:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (1.5,3.75)[/tex]
[tex](b_2,p_2) = (6,15)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{15 - 3.75}{6 - 1.5}[/tex]
[tex]m = \frac{11.25}{4.5}[/tex]
[tex]m = 2.5[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 3.75 = 2.5(b-1.5)[/tex]
[tex]p - 3.75 = 2.5b- 3.75[/tex]
[tex]p = 2.5b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]2.5 < 3.25[/tex]
Hence:
This equation is also less expensive than [tex]p = 3.25b[/tex]
Table C:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (2,7)[/tex]
[tex](b_2,p_2) = (4,14)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{14 - 7}{4 - 2}[/tex]
[tex]m = \frac{7}{2}[/tex]
[tex]m = 3.5[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 7 = 3.5(b - 2)[/tex]
[tex]p - 7 = 3.5b - 7[/tex]
[tex]p = 3.5b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3.5 > 3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table D:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (2.5,10)[/tex]
[tex](b_2,p_2) = (5,20)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{20 - 10}{5 - 2.5}[/tex]
[tex]m = \frac{10}{2.5}[/tex]
[tex]m = 4[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 10 = 4(b - 2.5)[/tex]
[tex]p - 10 = 4b - 10[/tex]
[tex]p = 4b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]4 > 3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table E:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (6, 22.5)[/tex]
[tex](b_2,p_2) = (12,45)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{45 - 22.5}{12 - 6}[/tex]
[tex]m = \frac{22.5}{6}[/tex]
[tex]m = 3.75[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 22.5 = 3.75(b - 6)[/tex]
[tex]p - 22.5 = 3.75b - 22.5[/tex]
[tex]p = 3.75b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3.75>3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table F:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (7, 21)[/tex]
[tex](b_2,p_2) = (14,42)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{42 - 21}{14 - 7}[/tex]
[tex]m = \frac{21}{7}[/tex]
[tex]m = 3[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p -21 =3(b -7)[/tex]
[tex]p -21 =3b -21[/tex]
[tex]p = 3b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3 < 3.25[/tex]
Hence:
This equation is less expensive than [tex]p = 3.25b[/tex]
