Question

Erin receives a 20% employee discount at the camera store where she works. She alsoreceives a $10 off the price on Wednesdays.a. Write a function e(p) that calculates Erin's new price after the employee discount(hint: what percent of the original price does she have to pay?)ep) =B. Write a function a(p) that calculates Erin's new price using her Wednesday discountonlya (p) =C. Write the function e(a(p))e a(p)) =D. What would Erin's final price be for a $400 camera she purchases on a Wednesday?

Answer 1

ANSWERS

A. e(p) = 0.8p

B. a(p) = p - 10

C. e(a(p)) = 0.8p - 8

D. $312

Step-by-step explanation

A. The employee discount is 20%. To the total price, which is 100%, we have to subtract the 20% to find the final price of the product. If the price is p, then the price after the employee discount would be,

`e(p)=(1-0.2)p=0.8p`

Hence, the function is e(p) = 0.8p

B. On Wednesdays, Erin gets a $10 discount on the price p of a product in the store, so if she buys on a Wednesday, she would pay a(p) = p - 10.

C. Now we have to find the function e(a(p)). This is a composition, where we have to replace p with a(p) in function e(p),

`e(a(p))=0.8a(p)=0.8(p-10)=0.8p-0.8\cdot10=0.8p-8`

Hence, the function is e(a(p)) = 0.8p - 8

D. If Erin buys a $400 camera on a Wednesday she will get both discounts: the employee discount and the Wednesdays discount. To find the final price for a selling price of p = 400, we have to use the function found in part C,

`e(a(400))=0.8\cdot400-8=320-8=312`

Hence, the final price for the $400 camera is $312, after both discounts.