QUESTION ABOUT LINEAR MODELS

Question

In a study by PricewaterhouseCoopers (PwC), it was found that DVD sales totaled $12.2 billion in 2013 (Lang, 2014). According to PwC, it’s expected that DVD sales will be $11.5 billion in 2014 and $8.7 billion in 2018 (PWC, 2014).
The study also projected an increase in sales from streaming videos. It’s expected that revenue will double by 2018, from $8.5 billion in 2014 to $17 billion in 2018.
1. What is the slope, including units, of the model for DVD sales?

Write a statement interpreting the meaning of the slope in the context of the problem.
2. Write an equation that represents the linear model for DVD sales. Let D = the sales of DVDs in billions of dollars, and t = the number of years after 2014.
3. What is the slope, including units, of the model for streaming videos?

Write a statement interpreting the meaning of the slope in the context of the problem.
4. Write an equation that represents the linear model for streaming videos. Let S = the total sales of streaming videos in billions of dollars, and t = the number of years after 2014.
5.In what year do you expect electronic home video sales to exceed DVD sales?

Answer 1

Erin, I hope I can still help!

 

1. The slope is change in y/change in x. Since the input (x) is the number of years and the output (y) is the total sales, the slope is $-2.8 billion/4 years, or $-.7 billion/year. Every year, sales go down $7 billion.

 

2. If we put it in slope-intercept form, D = -$.7 billion(t) + $11.5 billion

 

3. If it is doubling every 4 years, the slope is $8.5 billion/4 years, or $2.125 billion/year. Every year, sales go up $2.125 billion.

 

4. S = $2.125 billion(t) + $8.5 billion

 

5. -.7t + 11.5 < 2.125t + 8.5

            2.825t > 3

                      t > 1.06

 

In 2016, sales of streaming videos will exceed sales of DVDs.