A department store is offering a coupon for 28 ⁢ % off for any purchases over dollar-sign Baseline 100. Construct a piecewise function for the actual cost, C, of the purchase as a function of the original purchase price, P.

Question

A department store is offering a coupon for 28 ⁢ % off for any purchases over dollar-sign Baseline 100. Construct a piecewise function for the actual cost, C, of the purchase as a function of the original purchase price, P.

When 0<P</100 I got C=P. But I can't seem to get the formula for when P>100.

Answer 1

for 100 < P,

C(P) = 100 + 0.72(P-100)
or
C(P) = P - 0.28(P-100)

Answer 2

To determine the formula for P > 100, let's break down the problem.

When P > 100, the department store offers a 28% discount. This means the customer pays only 72% of the original price.

To calculate the actual cost, C, of the purchase when P > 100, we need to multiply the original price, P, by 72% or 0.72.

Therefore, the formula for C when P > 100 can be written as:
C = 0.72P

Let's summarize the piecewise function for C:

- When 0 < P < 100: C = P
- When P > 100: C = 0.72P

Now, depending on the original purchase price, P, you can use the appropriate formula to calculate the actual cost, C, of the purchase.