Question

PLEASE ANSWER ASAP

Answer 1

Answer:

$y=72.99+28.45(x-1)$

Step-by-step explanation:

Linear Modeling

Some situations in real life are bound to be modeled as mathematical functions. A model allows scientists and analysts to take decisions based on predicted values coming from those models.

To construct them we usually take or measure values of the variables of interest and find the general equation of the model. In this case, we'll find the relation between the service costs (y) of a cell phone provider and the number of months (x).

There are three points available: ( 1 , 72.99 ) , ( 2 , 101.44 ) , ( 3 , 129.89 ) and we only need two to find a function of the form

$y=c+d(x-1)$

We'll use the first two points and use the third point to verify the validity of the model. Let's plug in the first point:

$72.99=c+d(1-1)$

Operating

$72.99=c\\c=72.99$

Now for the second point

$101.44=72.99+d(2-1)$

Operating and rearranging

$d=101.44-72.99=28.45$

Our model is complete:

$\boxed{y=72.99+28.45(x-1)}$

Let's check the third point  ( 3 , 129.89 ) by plugging x=3

$y=72.99+28.45(3-1)=72.99+56.9=129.89$

The point belongs to the function.