Question

A restaurant served 25,000 customers in 2012. In 2014, the restaurant served 26,600 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.

Answer 1

Explanation:

y=25000(1+6,4%)^x

x=8 (2012-2020)

Answer 2

y = 800x + 25 000; 31 400 customers

Explanation:

A linear model has the form y = mx + b

There are two variables: the number of customers and the number of years since 2012. The number of customers depends on how long the restaurant has been operating.

m = (y₂-y₁)/(x₂ -x₁)

x₁ = 2012 – 2012 = 0; y₁ = 25 000

x₂ = 2014 – 2012 = 2; y₂ = 26 600

m = (26 600 – 25 000)/(2 - 0)

m = 1600/2

m = 800 customers/yr

The initial value (b) is the number of customers in 2012.

b = 25 000

The linear function is

y = 800x + 25 000

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Customers in 2020

x = 2020 -2012

x = 8 Insert into the formula

y = 800×8 + 25 000

y = 6400 + 25 000

y = 31 400 customers

The restaurant will serve 31 400 customers in 2020.