Question

Music, in 2001, full-length cassettes represented 3.4% of total music sales. Between 2001 and 2006, the percent decreased by about 0.5% per year.

a. Write an equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006

b. Find the percent of recorded music sold as full-length cassettes in 2004.

Answer 1

The linear equation to determine the percent of music sales for full-length cassettes for any year x between 2001 and 2006 is P(x) = 3.4 - 0.5x. For 2004, which is 3 years since 2001, the percent is calculated as 1.9%.

Step-by-step explanation:

To answer your questions on the decline in sales of full-length cassettes between 2001 and 2006, we can utilize linear equations. Here is how we can approach it:

Writing the Equation (Part a)

We know that in 2001, which we'll use as our base year (x=0), cassettes made up 3.4% of music sales. The percent decreased by approximately 0.5% per year thereafter.

We can set up a linear equation to represent this situation as follows:

P(x) = 3.4 - 0.5x

where:

P(x) is the percent of music sales from full-length cassettes in a given year.

x is the number of years since 2001.

Finding the Percent in 2004 (Part b)

To find the percent of recorded music sold as full-length cassettes in 2004, we substitute x=3 (since 2004 is 3 years after 2001) into our equation:

P(3) = 3.4 - 0.5(3)

P(3) = 3.4 - 1.5

P(3) = 1.9%

So, the percent of recorded music sold as full-length cassettes in 2004 was 1.9%.

Answer 2

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