The table below shows the number of days, y, needed to complete a project as a function of the number of full-time staff, x, working on the project. Which rational function best models the data in the table?

If you plug in an x-value into the different equations and check to see if the corresponding y-value is correct, then you can find the correct answer.

For y = x/72, you can check this by plugging in the x-value of 18.
18 / 72 = 0.25
When x was 18, y was 4, not 0.25.
So this is not the correct answer.

y = x / 18
y = 18 / 18
y = 1
When x was 18, y was 4, not 1.
So this is not the correct answer.

y = 18 / x
y = 18 / 18
y = 1
When x was 18, y was 4, not 1.
So this is not the correct answer.

y = 72 / x
y = 72 / 18
y = 4
When x was 18, y was 4.
So this is possibly the correct answer.
Let's test 2 other values to be sure.
y = 72 / x
y = 72 / 36
y = 2
When x was 36, y was 2.
This works.
y = 72 / x
y = 72 / 6
y = 12
When x was 6, y was 12.
This also works.
So this means y = 72 / x is the correct answer.

lisboa lisboa · Answer 2 · 2021-10-19T12:16:51+02:00

The rational function best models the data in the table

[tex]y=\frac{72}{x}[/tex]

Given :

The table below shows

the number of days, y, needed to complete a project as a function of the number of full-time staff, x, working on the project.

From the given table , y is the dependent variable and x is the independent variable

Lets check with each option

Lets take x=8 and y=9 . Substitute in each option and see which one satisfies the values

[tex]y=\frac{x}{72} \\x=8 and y=9\\9=\frac{8}{72}, false \\\\\\y=\frac{x}{18} \\9=\frac{8}{18}, false\\\\y=\frac{18}{x}\\9=\frac{18}{8}, false\\\\\\y=\frac{72}{x}\\9=\frac{72}{8}, true \\\\[/tex]

The rational function best models the data in the table

[tex]y=\frac{72}{x}[/tex]

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