Chapter 6.1, Problem 40PPS

a.

To determine

Draw the graph of the function. Also find the domain and range.

Explanation of Solution

Given: It is given in the question that x represents the number of years since $2012$ and y represents the number of units sold. Now, the number of tablets sold each year since ,in millions, can be modeled by the equation $y=12.5x+10.9$ .The number of laptops sold each year since $2012$ ,in millions, can be modeled by the equation $y=-9.1x+78.8$ .

Graph:

Interpretation: Here, the both equation $y=-9.1x+78.8andy=12.5x+10.9$ should be put in the graphic calculator, it gives the required graph.

Now, it is seen in the graph that both the graph intersect at a point $(3.144,50.194)$ .

Now, from the graph, The domain of each of these equations is the set of real numbers greater than or equal to $0$ .The range of each of these equation is the set of real numbers greater than or equal to $0$ .

b.

To determine

Find the year in which the tablet sales surpass laptop sales.

Answer to Problem 40PPS

The time at which the tablet sales surpass laptop sales is $2015$ .

Explanation of Solution

Given:

It is given in the question that x represents the number of years since $2012$ and y represents the number of units sold. Now, the number of tablets sold each year since $2012$ ,in millions, can be modeled by the equation $y=12.5x+10.9$ .The number of laptops sold each year since ,in millions, can be modeled by the equation $y=-9.1x+78.8$ .

Concept Used:

In this, use the concept of understanding the graph that obtained in above part.

Calculation: Here, the both line intersect at the point $(3.144,50.194)$ .

Since, the above point shows that the tablet sales surpass the laptop sales at $x=3.144$ ,so it is nearly in $2015$ i.e. after three years from $2012$ .

Conclusion:

The time at which it passes is $2015$ .