Digital Music Revenues

The total projected worldwide digital music revenues R, in millions of dollars, for the years 2005 through 2010 can be estimated by the function

R(x) = 170.7x^2 + 1373x + 1080 where x is the number of years after 2005.

(a) Find R(0), R(3) and R(5),represents. Explain what each value represents.

(b) Find r = R(x- 5).

(c) Find r(5), r(8), and r(10), and explain what each value represents.

(d) In the model r, what does x represent?

Let me see.

Part A

I simply replace x with 0, 3, and 5 but I have no idea what each value represents.

Part B

Can you set it up for me?

Part C

I think r(5) represent the year 2005, r(8) represents the year 2008 and r(10) represents the year 2010.

You say?

Part D

I need the model r to guess what x represents.

 

Part A:

Let's find the values of R(0), R(3), and R(5) by substituting the respective values of x into the function:

1. (0)=170.7(0)2+1373(0)+1080=1080R(0)=170.7(0)2+1373(0)+1080=1080
2. (3)=170.7(3)2+1373(3)+1080=5292.6R(3)=170.7(3)2+1373(3)+1080=5292.6
3. (5)=170.7(5)2+1373(5)+1080=11857.5R(5)=170.7(5)2+1373(5)+1080=11857.5

Each of these values represents the projected worldwide digital music revenues in millions of dollars for the corresponding years after 2005. So, (0)R(0) represents the revenue projection for the year 2005, (3)R(3) represents the revenue projection for the year 2008, and (5)R(5) represents the revenue projection for the year 2010.

Part B:

To find =(−5)r=R(x−5), we substitute −5x−5 for x in the function ()R(x):

=(−5)=170.7(−5)2+1373(−5)+1080r=R(x−5)=170.7(x−5)2+1373(x−5)+1080

Part C:

You're partially correct. (5)r(5) indeed represents the revenue projection for the year 2005 (since =(−5)r=R(x−5)). However, (8)r(8) represents the revenue projection for the year 2008 (not 2008, as that's (3)R(3)), and (10)r(10) represents the revenue projection for the year 2010 (not 2010, as that's (5)R(5)).

Part D:

In the model r, x represents the number of years after 2010. This is because =(−5)r=R(x−5), where −5x−5 represents the number of years after 2005. So, when we plug in values for x in r, we're looking at years after 2010.


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I am doing a self-study of math. I graduated in 1994. I am not a classroom student.