Question

An executive for the movie production company wants to create a function that models this data. . Create a function that can be used to model the data shown in the table . Be sure to define the variables and provide justification for your choice of function . Discuss any possible domain restrictions which should be placed on your model . Use your model to estimate the box office gross the company should expect in week 10 .

Answer 1

Functions can be modeled by equations, tables and graphs

• The equation that models the function is $y = \frac 14x +1$
• The domain of the function is the set of whole numbers
• The company should expect 4 box office gross in week 10

How to determine the function

From the question, we have the following ordered pairs

(x,y) = (0,1) and (4,2)

The function is a linear function.

So, we start by calculating the slope (m) using:

$m = \frac{y_2 - y_1}{x_2 -x_1}$

Substitute known values

$m = \frac{2 - 1}{4 - 0}$

$m = \frac{1}{4}$

The equation is then calculated as:

$y = m(x -x_1) +y_1$

This gives

$y = \frac 14(x -0) +1$

$y = \frac 14x +1$

The domain of the above function is the set of whole numbers

Substitute 10 for x, to calculate the number of box office gross for week 10

$y = \frac 14 * 10 +1$

$y = 3.5$

Approximate

$y = 4$

Hence, the company should expect 4 box office gross in week 10

Read more about linear functions at:

brainly.com/question/15602982