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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
BuyFindarrow_forward

Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

Social Media A Nielsen survey of 3000 American moviegoers aged 12−74 years found that 27% of them used social media to chat about movies in 2010. The percentage was 29% in 2011 and 31% in 2012. Let t = 0, t = 1, and t = 2 correspond to the years 2010, 2011, and 2012, respectively.

  1. a. Explain why the three points P1(0, 27), P2(1, 29), and P3(2, 31) lie on a straight line L.
  2. b. If the trend continues, what will the percentage of moviegoers who use social media to chat about movies be in 2014?
  3. c. Find an equation of L. Then use this equation to find and reconcile the result obtained in part (b).

Source: Nielsen survey.

(a)

To determine

To evaluate: The reason that the three points P1(0,27),P2(1,29),andP3(2,31) lie on a straight line.

Explanation

Given:

Nielsen survey of 3000 American moviegoers aged 12-74 years found that 27% of them used social media to chat about movie in 2010. The percentage was 29% in 2011 and 31% in 2012. Let t=0,t=1 and t=2 correspond to the years 2010, 2011, and 2012, respectively.

Formula used:

The formula to calculate the slope m and passes through the points (x1,y1)and(x2,y2) is,

m=(y2y1)(x2x1) (1)

The formula to calculate the equation of line has slope m and passes through the point (x1,y1) is,

m=(yy1)(xx1) (2)

Calculation:

The given point P1(0,27),P2(1,29),and

(b)

To determine

To evaluate: The trend continues, what will the percentage of moviegoers who use social media to chat about movie be in 2014?

(c)

To determine

To evaluate: An equation of L , Then use this equation to find and reconcile the result obtain in part (b).

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