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 integers or decimals in any numbers in the equation. round to three decimal places as needed)

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	actual revenue	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	\square	\square
2014	2047	\square	\square

help me solve this
view an example
get more help

question 14 of 20
back
clear all
check answer

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: Identify quadratic model

First, calculate the quadratic regression model from the data. Using the given actual revenue data, the quadratic model is:
$$y = -4.87x^2 - 192.91x + 7286.52$$

Step3: Calculate 2013 predicted revenue

Substitute $x=13$ into the model:
$$y = -4.87(13)^2 - 192.91(13) + 7286.52$$
$$y = -4.87(169) - 2507.83 + 7286.52$$
$$y = -823.03 - 2507.83 + 7286.52 = 3955.66 \approx 3956$$

Step4: Calculate 2013 actual-predicted difference

Subtract predicted from actual revenue:
$$2317 - 3956 = -1639$$

Step5: Calculate 2014 predicted revenue

Substitute $x=14$ into the model:
$$y = -4.87(14)^2 - 192.91(14) + 7286.52$$
$$y = -4.87(196) - 2700.74 + 7286.52$$
$$y = -954.52 - 2700.74 + 7286.52 = 3631.26 \approx 3631$$

Step6: Calculate 2014 actual-predicted difference

Subtract predicted from actual revenue:
$$2047 - 3631 = -1584$$

Answer:

Year	Actual Revenue	Predicted Revenue	Difference
2009	4440	4515	-75
2010	3649	3723	-74
2011	3112	3086	26
2012	2669	2604	65
2013	2317	3956	-1639
2014	2047	3631	-1584

Quadratic model: $\boldsymbol{y = -4.87x^2 - 192.91x + 7286.52}$ (where $x$ = years since 2000, $y$ = revenue in millions of dollars)