Problem

Volume discount. Assume that the volume discounts in Table apply to the entire purchase. T...

Volume discount. Assume that the volume discounts in Table apply to the entire purchase. That is, if the volume x satisfies $300 ≤ x < $1,000, then the entire purchase is discounted 3%. If the volume x satisfies $1,000 ≤ x < $3,000, the entire purchase is discounted 5%, and so on.

(A) If x is the volume of a purchase before the discount is applied, then write a piecewise definition for the discounted price D(x) of this purchase.


(B) Use one-sided limits to investigate the limit of D(x) as x approaches $1,000. As x approaches $3,000.

Table Volume Discount (excluding tax)

Volume ($x)

Discount Amount

$300 ≤ x < $1,000

3%

$1,000 ≤ x < $3,000

5%

$3,000 ≤ x < $5,000

7%

$5,000 ≤ x

10%

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