Answer
a) $y=219n+142$
b) 2006; $580$ million
Work Step by Step
a) Let's note:
$n$=the number of years after 2004
We can model the sale of digital tracks, $y$, by using a linear function $y=an+b$.
The slope of the function, $a$, is the average rate of growth: 219 per year:
$a=219$
The term $b$ is the number of tracks sold in 2004: 142.
$b=142$
The function is:
$y=219n+142$
b) We have to solve the system:
$\begin{cases}
y=219n+142\\
95n+y=770
\end{cases}$
Use the substitution method:
$95n+219n+142=770$
$314n+142=770$
$314n+142-142=770-142$
$314n=628$
$n=\dfrac{628}{314}$
$n=2$ years
The year will be:
$2004+2=2006$
The number of digital track/albums sold in 2006 is:
$y=219\cdot 2+142$
$=580$ million
