Question

The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century. Let x = number of years since 1900, and y = pounds per person.
Year
Pounds Consumed
1902
1.959
1924
6.373
1946
7.29
1982
15.817

Answer 1

That's nice.

Answer 2

It was supposed to be a table, but the format is all messed up so the years are just above the number of pounds consumed

Answer 3

Oh yeah, fair enough. Still, there's no question or anything.

Answer 4

Oh crap sorry, you're supposed to find the best cubic model that fits the data

Answer 5

Oh. Well, you first say you have a general cubic: x^4 + ax^3 + bx^2 + cx + d. (you don't need a coefficient in front of the first term because you could just divide through to eliminate that one)

You have four unknown coefficients. You also have four data points that you want this cubic to fit into. So now you need to punch in that data to work out the coefficients. For example, when x=1902, you need to have that the cubic gives 1.959.

Answer 6

And actually this turns into a linear problem, because you know what x is each time. It's just the coefficients, which are linear, that are unknown. So I'd say you'd be best writing this out as a matrix inversion problem, to work out the coefficients.

Answer 7

we are looking for a cubic eh; so 3 equations in 3 unknowns; or ...

we can define a general equation to match the given inputs

Answer 8

Oh, sorry, yeah cubic. Just rewrite as general cubic, not quartic.

Answer 9

a. y = 0.00989x 3 − 0.0000872x 2 + 1.192x + 0.403
b. y = −0.0000872x 3 + 0.00989x 2 − 0.403x − 1.192
c. y = −0.0000872x 3 − 0.00989x 2 − 0.403x + 1.192
d. y = 0.0000872x 3 − 0.00989x 2 + 0.403x + 1.192


These are the answer options

Answer 10

2, 1.959
24, 6.373
46, 7.29
82, 15.817

prolly simplest to setup a matrix and rref it

rref{{2^3,2^2,2,1,1.959},{24^3,24^2,24,1,6.373},{46^3,46^2,46,1,7.29},{82^3,82^2,82,1,15.817}}

Answer 11

http://www.wolframalpha.com/input/?i=rref%7B%7B2%5E3%2C2%5E2%2C2%2C1%2C1.959%7D%2C%7B24%5E3%2C24%5E2%2C24%2C1%2C6.373%7D%2C%7B46%5E3%2C46%5E2%2C46%2C1%2C7.29%7D%2C%7B82%5E3%2C82%5E2%2C82%2C1%2C15.817%7D%7D

that gives you your coeefs

Answer 12

man what an annoying problem
http://www.wolframalpha.com/input/?i=polynomial+%282%2C1.959%29%2C%2824%2C6.373%29%2C%2846%2C7.29%29%2C%2882%2C15.817%29

Answer 13

@mayankdevnani wolf will actually do it for you

Answer 14

type in "polynomial" give 4 ordered pairs and out comes a third degree

Answer 15

i can't begin to imagine doing this by hand with all the decimals. what a pain