Customers at a supermarket have been increasing at...

Question

Customers at a supermarket have been increasing at a linear rate. In 2011 the number was 570,000. In 2012 was 730,000 if y represent the number of customers visiting the supermarket per year and x rep. time measured in years (x=0 for 2010)

i) Determine the linear estimating function of the number of customers visiting the supermarket

ii) Interpret the meaning of the slope

Answer 1

Let set variable x to be number of years since 2010. Then, x = 0 will be 2010, x = 1 will be 2011, x = 2 will be 2012.

We assumed linear model. This means that we can find the slope by finding the ratio Δy/Δx. To use smaller numbers, we will express customers in thousands. In year 2011 there were 570 thousands, so y = 570. In 2012 y = 730.

Slope = Δy/Δx

= (730 - 570)/(2 - 1) = 160.

The slope shows how many more customers the supermarket gain in a year. 160 means each year the supermarket will have 160000 more customers compared to the year before.

The linear function (in point slope form):

y - y_o = slope (x - x_o)

We will use year 2011 in the above equation - (1, 570):

y - 570 = 160(x - 1)

...

y = 430 + 160x.

The linear model is expressed above. 430 is the base value (year 2010). 160 shows increase the number of customers in thousands per year is 160.

The way you can check the work is to calculate the given information using the model above. For x = 1 we should have y = 570, and for x = 2 -> 730.