Function word problem please HELP

Question

The Celestial Bakery currently sells an average of 750 wedding cakes per month and charges an average of $200 per cake. Market research indicates that for every $5 increase in the price of a cake, the bakery will sell 15 fewer cakes per month, and for every $5 decrease in the price of a cake, the bakery will sell 15 more cakes per month. Let p= the price per cake and let N =the number of cakes sold per month. What type of function would best model N as a function of p? Explain. Find and simplify an equation to represent N as a function of p and explain your procedure. 

Answer 1

The change in the number of cakes is ΔN/Δp = -15/5 = -3 (cakes/dollar) at the current price.

ΔN = (-3)Δp = -3Δp

The change in p from the current price is:

Δp = p-200.

The change in the number of cakes is that difference times the rate of change: -3.

N becomes the current sales volume plus ΔN.

N = 750 - 3(Δp)

N = 750 - 3(p-200)

N = 750 + 600 - 3p

N = 1350 - 3p

 

Check: Under current business conditions:

N = 1350 - 3(200) = 1350-600 = 750

At p = 205:

N = 1350 - 3(205) =  1350-615 = 735