Apaperback sells for $12. the author is paid royalties of 10% for the first 10,000 copies sold and 15% on any additional copies. write a piece wise function

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.