Answer:
[tex]r(x)=\left\{\begin{array}{lcl}1.20x&\text{for}&x\le 10000\\1.80x-6000&\text{for}&x>10000\end{array}\right.[/tex]
Step-by-step explanation:
Royalty per book for the first 10,000 is $12·0.10 = $1.20. That is, for sale of x books (x ≤ 10000), the royalty is ...
1.20x
So, on 10,000 copies, the royalty is ...
10,000 · $1.20 = $12,000
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After that, the royalty is $12·0.15 = $1.80 per book. If x is the number of books sold, the number of books more than 10,000 is ...
x - 10,000
and the additional royalty (above $12000 for 10,000 books) will be ...
$1.80(x -10,000)
When this is added to the royalty for the first 10,000 books, the expression (for x > 10000) can be simplified to ...
12000 +1.80(x -10000) = 12000 +1.80x -18000 = 1.80x -6000
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So, the piecewise function has two pieces: one for numbers of books below 10,000, and one for numbers of books above 10,000.
[tex]r(x)=\left\{\begin{array}{lcl}1.20x&\text{for}&x\le 10000\\1.80x-6000&\text{for}&x>10000\end{array}\right.[/tex]
