From 2005 through 2014, the number of music CDs sold in the United States declined each year by approximately 15%

Question

From 2005 through 2014, the number of 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?

Accepted Answer

Choice B is correct. A model for a quantity C that decreases by a certain percentage per time period t is an exponential equation in the form , where I is the initial value at time for r % annual decline. It&rsquo;s given that C is the number of millions of CDs sold in the United States and that t is the number of years after 2005. It&rsquo;s also given that 600 million CDs were sold at time , so . This number declines by 15% per year, so . Substituting these values into the equation produces , or . Choice A is incorrect and may result from errors made when representing the percent decline. Choices C and D are incorrect. These equations model exponential increases in CD sales, not exponential decreases.

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