Question
From 2005 through 2014 , the number music CDs sold in the United States declined each year by approximately 15% of the number sold the preceding year. In 2005 , approximately 600 million CDs were sold in the United States. Of the following, which best models C, the number of millions of CDs sold in the United States, t years after 2005 ?
- C = 600 (0.15)t
- C = 600 (0.85)t
- C = 600 (1.15)t
- C = 600 (1.85)t
The correct answer is: C = 600 (0.85)t
The reduction of 15% is observed in this when compared to previous years .
Then the percentage of cd sold next year will be (100 - 15)% of this year.
The no. of CD's sold in 2005 is 600.(in millions)
The no. of CD's sold in 2006 is 85% of CD's sold in 2005 = 600(0.85)(in millions)
The no. of CD's sold in 2007 is 85% of CD's sold in 2006 = 600(0.85)2 (in millions)
The no. of CD's sold in 2008 is 85% of CD's sold in 2007 = 600(0.85)3 (in millions)
and so on …
This results in a Geometric progression . where a = 600 and r = 0.85
C after t year = 600 (0.85)t
∴In this pattern the no.of CD’s sold after t years from 2005 is 600(0.85)t
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