Question

Use the equation r =2.1x^2 -14.3x +35, where x is the number of years after 2000, to determine the revenue from the sales of U.S. Recorded albums in the years 2000, 2001, 2002, 2003, 2005, 2010 and 2018. How would you describe the trend in the revenue from albums? To what do you attribute this?

Answer 1

Answer:

Step-by-step explanation:

Given that:

$r = 2.1x^2 - 14.3x + 35$

For year 2000; x = 0

So; $r (0) = 2.1(0)^2 - 14.3(0) + 35$

$r (0) = 35$

For year 2001; x = 1

$r (1) = 2.1(1)^2 - 14.3(1) + 35$

$r (1) =22.8$

For year 2002; x = 2

$r (2) = 2.1(2)^2 - 14.3(2) + 35$

$r (2) = 14.8$

For year 2003; x = 3

$r (3) = 2.1(3)^2 - 14.3(3) + 35$

$r (3) = 11$

For year 2005; x = 5

$r (5) = 2.1(5)^2 - 14.3(5) + 35$

r(5) = 16

For year 2010; x = 10

$r (10) = 2.1(10)^2 - 14.3(10) + 35$

$r(10) = 102$

For year 2018; x =18

$r(18) = 2.1(18)^2 - 14.3 (18) + 35$

$r(18) = 458$

Thus, the table can be presented as seen below.

Year      2000     2001     2002     2003     2005     2010     2018

x               0             1             2            3           5            10         18

r(x)          35          22.8        14.8        11            16         102      458

SO, we will notice that the revenue for the albums starts decreasing and when it reaches the minimum, it started increasing with increasing x.

The attribute behind this trend is because the revenue function r(x) typically implies that it is a quadratic function.