5. The market share of eBooks (the percentage of revenue from all books) was 8.3

Question

5. The market share of eBooks (the percentage of revenue from all books) was 8.3% in 2010 and has grown by about 108% per year since then (Source: German Book Office New York) That is, each year the market share is about 2.08 times the previous year's market share a. Let M f(t) be the market share of eBooks at t years since 2010. Find an equation of f. b. What is the M-intercept? What does it mean in this situation? c. What is the base b of f() ab'? What does it mean in this 9, s situation? d. Predict the market share in 2013. Assuming the revenue of all books will be $5 billion in that year, predict the revenue from eBooks.

Explanation / Answer

5. The market share of e Books is 8.3 % in 2010 and in each year thereafter, the market share of e Books is 2.08 times the previous year’s market share. This pattern represents a geometric series with 8.3 as the 1st term and common ration 2.08 ( in percentages).

a. The nth term of the geometric series with the 1st term a and common ratio r is arn-1. Hence M = f(t) = 8.3*(2.08)t (t years since 2010 is the (t+1)th term).

b. The M-intercept is where t = 0. Then M =8.3%. It represents the market share of e Books in 2010.

c. The base of f(t) = abt is b. It means the no. of times that the market share of e Books grows, each year, since 2010.

d. In 2013, t = 3 so that the market share of e Books in 2013 is 8.3 *(2.08)3 = 74.69 %.If the revenue from all Books in 2013 is $ 5 billion, then the revenue from eBooks in 2013 will be 5*74.69 = $ 3.7345 billion = $ 3734.5 million.    

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.