Question

Music The numbers of download music singles D (in millions) from 2004 through 2009 can be modeled by

D = -1671.88 + 1282 In t
where t = 4 corresponds to 2004. Find the rates of change of the number of download music singles in 2005 and 2008.

Answer 1

Answer: About 200.85 million per year.

Explanation:

Given : Music The numbers of download music singles D (in millions) from 2004 through 2009 can be modeled by
`D (t)= -1671.88 + 1282 \In t`

,where t = 4 corresponds to 2004.

For 2005 , t= 4+1=5 (2005=2004+1)

For 2008 , t= 4+4=8 (2008=2004+4)

At t= 5,
`D (5)= -1671.88 + 1282 \ln5`

`D (5)= -1671.88 + 1282 (1.6094379)=391.4193878\approx391.42`

At t= 8 ,
`D (8)= -1671.88 + 1282 \ln8`

`D (8)= -1671.88 + 1282 (2.07944154168)=993.964056434\approx993.96`

Now , the rates of change of the number of download music singles in 2005 and 2008. would be
`(D(8)-D(5))/(8-5)=(993.96-391.42)/(8-5)`

`=(602.54)/(3)=200.846666667\approx200.85`

The rate of change of the number of download music singles in 2005 and 2008 is about 200.85 million per year.