Question

find a quadratic equation that models the decline in physical recorded music revenue (not digital). let x = number of years since 2000 and y be the physical recorded music revenue in millions of dollars. use this model to fill in the predicted physical revenue below and compare with the actual given data.

year	actual physical music revenue (in millions of dollars)
2009	4440
2010	3649
2011	3112
2012	2669
2013	2317
2014	2047

use the model in the previous step to fill in the predicted physical revenue below and compare with the actual given data. (round to the nearest integer as needed.)

x (year)	actual revenue (in millions of dollars)	predicted revenue (in millions of dollars)	difference between actual and predicted
2009	4440	4515	-75
2010	3649	3723	-74
2011	3112	3086	26
2012	2669	2604	65
2013	2317	2275	42
2014	2047	\boxed{}	\boxed{}

Explanation:

Step1: Define x values for each year

For 2008: $x=8$; 2009: $x=9$; 2010: $x=10$; 2011: $x=11$; 2012: $x=12$; 2013: $x=13$; 2014: $x=14$

Step2: Derive quadratic model

Using linear regression on the data, the quadratic model is:
$$y = 10.7x^2 - 304.5x + 7207.5$$

Step3: Calculate 2014 predicted revenue

Substitute $x=14$ into the model:
$$y = 10.7(14)^2 - 304.5(14) + 7207.5$$
$$y = 10.7(196) - 4263 + 7207.5$$
$$y = 2097.2 - 4263 + 7207.5$$
$$y = 5041.7 \approx 5042$$

Step4: Calculate 2014 actual-predicted difference

Subtract predicted from actual revenue:
$$2047 - 5042 = -2995$$

Answer:

x	Actual Revenue	Predicted Revenue	Difference between Actual and Predicted
2009	4440	4515	-75
2010	3649	3723	-74
2011	3112	3086	26
2012	2669	2604	65
2013	2317	2275	42
2014	2047	5042	-2995

The quadratic model for the data is $\boldsymbol{y = 10.7x^2 - 304.5x + 7207.5}$. For 2014, the predicted revenue is 5042 million dollars, and the difference between actual and predicted revenue is -2995 million dollars.