Question 1112773: Pete Zarilla sells 10-inch pizzas for $4.30, 12 inch pizzas for 5.88, and 14 inch pizzas for 7.78. Assume that the price is a quadratic function of the diameter.
a) Write the particular equation expressing price in terms of diameter.
b)predict the price of a 5 inch pizza.
c) If a pizza sells for $20, what would you expect the diameter to be?
d) what is the significance of the fact that the price- intercept is greater than zero? Suggest what it might represent.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 4.30=ax^2+bx+c
x=5
4.30=25a+5b+c
5.88=36a+6b+c
7.78=49a+7b+c
1.58=11a+b
1.90=13a+b
0.32=2a
a=0.16
b=-0.18
c=1.2
C=0.16x^2-0.18x+1.2, in dollars, with x= radius.
when diameter is 5, x=2.5
C=1-0.45+1.20=$1.75
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20=0.16x^2-0.18x+1.2
0=0.16x^2-0.18x-18.8
x=(1/0.32)(0.18+/- sqrt(0.0324+12.032); sqrt term=3.47
x=3.125*3.65, only positive root
=11.41
diameter is 22.82 inches.
Can do a rough check by using C=Kx^2, and K is about 0.15 for simple cost is a function of radius squared function (a little larger for smaller). That would be $19.52, which is a reasonable check.
The price intercept >0 could be considered the contribution of the overhead for making a pizza, having the ingredients there, the building, etc.
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