A company sells embroidered apparel. The volume discounts offered by the company are shown below, where x is the volume of a purchase in dollars.

Volume ($x) Discount Amount

$300 x < $1000 3%

$1000 x < $3000 5%

$3000 x < $5000 7%

$5000 x 10%

Assume the volume discounts in Table 1 apply only to that portion of the volume in each interval. That is, the discounted price for a $4000 purchase would be computed as follows:

300 + .97(700) + .95(2000) +.93(1000) = 3,809

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

b. Use one sided limits to investigate the limit of P(x) as x approaches $1000. What about as x approaches $3000?