Answer:
[tex]4\frac{1}{11}[/tex] hours
Explanation:
Given
See attachment for graph
First, we determine the equation of the graph.
Pick any two points from the graph
[tex](h_1,d_1) =(18,168)[/tex]
[tex](h_2,d_2) =(36,366)[/tex]
Calculate the slope (m)
[tex]m = \frac{d_2 - d_1}{h_2 -h_1}[/tex]
This gives:
[tex]m = \frac{366 - 168}{36 -18}[/tex]
[tex]m = \frac{198}{18}[/tex]
[tex]m = 11[/tex]
The equation is then calculated as:
[tex]d = m(h - h_1) + d_1[/tex]
This gives:
[tex]d = 11(h - 18) + 168[/tex]
Open bracket
[tex]d = 11h - 198 + 168[/tex]
[tex]d = 11h-30[/tex]
So, the number of hours to earn $15 is:
[tex]d = 11h-30[/tex]
[tex]15 = 11h -30[/tex]
Collect like terms
[tex]11h = 15 + 30[/tex]
[tex]11h = 45[/tex]
Solve for h
[tex]h = \frac{45}{11}[/tex]
[tex]h = 4\frac{1}{11}[/tex]
