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The table to the right shows the volume discounts offered by a​ company, where x is the volume of a purchase in dollars. Assume that the volume discounts in the table apply to the entire purchase. That​ is, if the volume x satisfies $300≤x<$1,000​, the entire purchase is discounted 4%. Answer ​a) and ​b) below.
$300≤x<$1,000
$1,000≤x<$3,000
$3,000≤x<$5,000
$5,000≤x
4%
5%
6%
10%

Volume Discount
(Excluding tax)
Volume($x)
Discount Amount
Question content area bottom
Part 1
​a) If x is the volume of a purchase before the discount is​ applied, write a piecewise definition for the discounted price​ D(x) of this purchase.
D(x)= x if 0≤x<300 enter your response here if 300≤x<1,000 0.95x if 1,000≤x<3,000 enter your response here if 3,000≤x<5,000 0.90x 5,000≤x

Sagot :

The piecewise function for the discounted price of the purchase is given by:

  • D(x) = 0.96x, 300≤x<1,000.
  • D(x) = 0.95x, 1,000≤x<3,000.
  • D(x) = 0.94x, 3,000≤x<5,000.
  • D(x) = 0.9x, 5,000≤x.

What is a piecewise function?

A piecewise function is a function that has different definitions, depending on the input.

For $300≤x<$1,000, the discount is of 4%, hence the discounted price is 96% of the original price, that is:

D(x) = 0.96x, 300≤x<1,000

For $1,000≤x<$3,000, the discount is of 5%, hence the discounted price is 95% of the original price, that is:

D(x) = 0.95x, 1,000≤x<3,000.

For $3,000≤x<$5,000, the discount is of 6%, hence the discounted price is 94% of the original price, that is:

D(x) = 0.94x, 3,000≤x<5,000.

For $5,000≤x, the discount is of 10%, hence the discounted price is 90% of the original price, that is:

D(x) = 0.9x, 5,000≤x.

More can be learned about piecewise functions at https://brainly.com/question/27262465

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