Question

A restaurant served 27,000 customers in 2012. In 2014, the restaurant served 28,400 customers. Write a linear model that represents the number y of customers that the restaurant serves x years after 2012. Use the model to predict the number of customers that the restaurant will serve in 2020.

i just need the linear model is y=

Answer 1

The model that represents number y of customers that the restaurant serves x years after 2012 is y = 700x + 27000

The restaurant will serve 32600 customers in 2020

Since 2012 is the initial year:

In year 2012, x₁ = 0

Number of customers served in 2012, y₁ = $27000

In year 2014, x₂ = 2

Number of customers served in 2014,

y₂ = $28400

The slope can be calculated using the formula:

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

$m \: = \frac{28400 - 27000}{2 - 0}$

m = 700

The model is linear and it will be given by the general equation:

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

$y - 27000 = 700(x - 0)$

$y = 700x + 27000$

The linear model is:

y = 700x + 27000

In 2020, x = 8

The number of customers the restaurant will serve in 2020 will be calculated by substituting

x = 8 into the model

y = 700(8) + 27000

y = 5600 + 27000

y = 32600

The restaurant will serve 32600 customers in 2020

Learn more here:https://brainly.com/question/19540800