Question 1189168
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Part (a)


You will need a graphing calculator or other similar form of technology to determine the regression equation. It can be done by hand, but such a process is tedious busywork.


You should find the cubic regression equation is approximately {{{y = -45.69x^3 + 1005.15x^2 - 7567.95x + 20716.83}}}


Answer:
a = -45.69
b = 1005.15
c = -7567.95
d = 20716.83


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Part (b)


Plug in x = 4.35 and simplify
{{{y = -45.69x^3 + 1005.15x^2 - 7567.95x + 20716.83}}}


{{{y = -45.69(4.35)^3 + 1005.15(4.35)^2 - 7567.95(4.35) + 20716.83}}}


{{{y = 3055.32311625}}}


{{{y = 3055}}}


Answer: 3055 boxes


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Part (c)


Plug in y = 366 and solve for x. You'll need a graphing calculator again.


Effectively, you are looking where the horizontal line y = 366 and the cubic curve {{{y = -45.69x^3 + 1005.15x^2 - 7567.95x + 20716.83}}} intersect. 
When using a graphing calculator, that location is approximately (9.5, 366)


Answer: $9.50 per box


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Part (d)


Like with part (c), we'll use a y value to determine x. 
This time, we use y = 0 to find x.


Use the root finder feature on your calculator to determine that the x intercept is approximately (9.88, 0)


Answer: $9.88 per box
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