A department store is offering a coupon for 21% off for any purchases over $100.
How much would you spend for a $100 purchase?
You would spend $100.
You would spend $79 on a purchase of $100.01
You would spend $79.8 on a purchase of $101.00
You would spend $87.69 on a purchase of $111.00
Construct a formula a piecewise functiom for the actual cost, C, of the purchase as a function of the original purchase price, P.
C=__?__,if 0 < P </ 100.
C=__?__, if P>100
C = 0.79P, P>100.
To construct a formula for the actual cost of the purchase as a function of the original purchase price, we need to consider the two scenarios based on the value of P.
1. If 0 < P < 100:
In this case, since the purchase price is less than $100, the coupon is not applicable. Therefore, the actual cost (C) would be equal to the original purchase price (P).
Formula: C = P
2. If P > 100:
In this case, the coupon is applicable for a 21% discount. To calculate the actual cost (C), we need to subtract 21% of the original purchase price (P) from the original price.
Formula: C = P - (0.21 * P)
=> C = P - 0.21P
=> C = (1 - 0.21)P
=> C = 0.79P
Combining both scenarios, we can write the piecewise function for the actual cost, C, as a function of the original purchase price, P:
C = { P, if 0 < P < 100,
0.79P, if P > 100 }