Question

102. Market Share: Smartphones The following graph shows the approximate market shares, in percentage points, of smartphones using Apple's iOs operating system and Microsoft's Windows Phone operating system, from the second quarter of 2011 to 2014. (t is time in years andt 0 represents the second quarter of 2010.) Market share (%) 20 a 18 16 14 17 10 Windows Phone 4 2. 21 3 Let I (t) be the iOS market share at time t, and let W (t) be the Windows Phone market share at time t. a. What does the function I - W measure? What does its derivative (I W) measure? b. The graph suggests that, on the interval [1, 4], I - W is A. increasing. B. decreasing. C. increasing, then decreasing. D. decreasing, then increasing. c. The two market shares are approximated by 0.7t-5.2t +8.9t +14 I (t) iOS: Windows Phone: W (t)-0.7t +3.9t -2. Compute (I W)', stating its units of measurement. On the interval [1, 4), (I-W is A. positive. B. negative. C. positive, then negative. D. negative, then positive. How is this reflected in the graph, and what does it mean about the market shares of the iOS and Windows Phone operating systems? d. Compute (I- W) (2). Interpret your answer.

Answer 1

a) I(t) - W(t) measures the difference of the market share of iPhone and Windows phone

b) It suggests that in the interval [1,4], I-W function is decreasing, then increasing

c)

2 0.7-5-21+8 -9t t(44 TH O777 4 3-9t -2 Wit) O7f-O 45+5t + 16 2 2-1t-9t 5

2- 2 4

So it is negative then positive

In the graph we can see that the difference of market shares first decreases and then slightly increases

d) (I-W)'(2)=-4.6 so that at this point, the difference between the market shares is decreasing (windows phones are starting to gain iPhone market share)