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Nonlinear functions SAT question
Math · Advanced Math · Medium · Answer it here, explanation included.
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?
ExplanationShow
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’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’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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