Question

In a certain​ country, total alcoholic beverage sales are reported throughout the year. Sales were reported as ​$112.5 billion at the beginning of 2001 and ​$139.9 billion at the beginning of 2003. ​

(a) Let the​ x-axis denote time and the​ y-axis denote the amount of alcohol sales​ (in billions). Let x=0 correspond to 2001. Fill in the​ blanks: The given data is represented by the points ​(_,112.5​) and ​(2​,__). ​

(b) Find the linear equation determined by the two points in part​ (a). ​

(c) Use the equation in part​ (b) to estimate the alcohol sales produced in 2002. ​

(d) If the model remains​ accurate, in what year will reported alcohol sales reach ​$150 ​billion?

Answer 1

a) Here, we are given that 2001 corresponds to the point 0. Therefore the sales are reported here as $112.5 billion at the beginning of 2001. Therefore the point here is given as: ( 0, 112.5 )

Now for year 2003, the point on x axis would be X = 2 as it is 2 points to the right of 2001. Therefore the second point here would be given as: ( 2, 139.9)

b) The linear equation here could be obtained by using the equation of line using two points. This is obtained here as:

Therefore the equation of line here is given as:

c) Now for year 2002, the point on the x axis would be 1 and therefore the predicted sales is computed as:

d) Here we will first find x for y = 150 as:

Therefore the reported alcohal sales would reach $150 billion in the year 2001 + 2.73 that is in the year 2004