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. What cubic model best fits this data?

Year Pounds Consumed
1902 1.959
1924 6.373
1946 7.29
1982 15.817
A. y = 0.00989x3 - 0.0000872x2 + 1.192x + 0.403
B. y = -0.0000872x3 + 0.00989x2 - 0.403x - 1.192
C. y = -0.0000872x3 - 0.00989x2 - 0.403x + 1.192
D. y = 0.0000872x3 - 0.00989x2 + 0.403x + 1.192

Answer 1

can you help me.?

Answer 2

yes just a second.

Answer 3

okayy thanks

Answer 4

ok. so right now you have a table that shows the year. but what you want is to rewrite that table with the years since 1900.

Answer 5

okay how would i do that can you show me

Answer 6

then after that, try plugging those numbers into each equation.

Answer 7

if the year is 1902, then how many years have passed since 1900?

Answer 8

2

Answer 9

so for the year 1902 you have x=2

Answer 10

okay so do i plug that into something.?

Answer 11

you can just plug 2 into each of those equations and see what they give you. That's a time consuming way to do it, but the easiest.

Answer 12

so i would pulg it inot this 1st right
A. y = 0.00989x3 - 0.0000872x2 + 1.192x + 0.403

Answer 13

into*

Answer 14

yup. see what each one gives you.

Answer 15

okay so i just plug it in where i see x right..?

im sorry i have no math skills lol. but im trying

Answer 16

yes, x = 2 so you plug it in where you see x.

Answer 17

im sorry but that doest help me figure it out it just adds a 2 to everything :/

Answer 18

A. y = 0.0098923 - 0.000087222 + 1.1922 + 0.403

Answer 19

1.605005078
thats what i got :x

Answer 20

i was assuming that the you copied and pasted this and the first function was\[y = 0.00989x^3 - 0.0000872x^2 + 1.192x + 0.403\]

Answer 21

yessss

Answer 22

http://gyazo.com/3b5078294c16e643ba5aebea38b18ff6

Answer 23

thats the entire problem

Answer 24

yeah so that means you have \[0.00989\times 2^3 -0.0000872\times2^2+ \dots\]

Answer 25

okay so i would just multiply from this point

Answer 26

yes. you plug it in. what you are trying to do is see which equation matches the data in the table.

Answer 27

the blue dots in this graph is the data provided in the table, and the four functions are plotted. notice how one fits the data nicely? your goal is to figure out which one does. The easiest way to do this is to just check each formula at one point, in this case x=2.

Answer 28

If you practice enough math, you can figure out quicker ways to do this, but they are more difficult than just plugging in...

Answer 29

okay so im guessing that from looking at the graph that the answer is pink line

Answer 30

which would be answer C

Answer 31

wait what? why the pink line? and I did not tell you which line corresponded to which function. I was just trying to help you understand what you are doing.

Answer 32

okay

Answer 33

i was guessing

Answer 34

here. the first one would look like this
\[0.00989\times 2^3 - 0.0000872 \times 2^2 + 1.192\times 2 + 0.403=2.866\]

Answer 35

does that match the data given to you?

Answer 36

no

Answer 37

ok. so try doing that with the next equation on the list of answers. see if it matches your data

Answer 38

it doesnt

Answer 39

what number did you get?

Answer 40

186

Answer 41

you did something wrong. you know the order of operations right?

Answer 42

yes

Answer 43

check your calculations again then.