You got it backwards
let y = ax^3 + bx^2 + cx + d
where x is the year, and y is the consumption
you substituted in the wrong variables
let's set 1915 as x=0
1922 -------> x = 7
1946 -------> x = 31
1991 -------> x = 76
so
0 + 0 + 0 + d = 4.156
343a + 49b + 7c + d = 4.857
29791a + 961b + 31c + d = 7.16
438976a + 5776b + 76c + d = 29.989
this would be a horrible system to solve,
I have found a webpage that solves a linear system of equations up to 5by5
http://math.cowpi.com/systemsolver/4x4.html
it gave me
a = 0.00008022
b = -0.00318329
c = 0.1184952015
d = 4.156
so
y = 0.00008022x^3 -0.00318329x^2 +0.1184952015x + 4.156
remember, x is the time since 1915
(using my calculator, I actually tested these values, they work for all 4 equations !! )
Really need help with one problem.
The table shows the annual consumption of cheese per person in the United States for selected years in the 19th century. What cubic model best fits this data?
Year Pounds Consumption
1915 4.156
1922 4.857
1946 7.16
1991 29.989
Not sure but do you set it up like this:
ax^3+bx^2+cx^+d=y
a(4.156)^3+b(4.156)^2+c(4.156)+d=1915
a(4.857)^3+b(4.857)^2+c(4.857)+d=1922
a(7.16)^3+b(7.16)^2+c(7.16)+d=1946
a(29.989)^3+b(29.989)^2+c(29.989)+d=1991
Now don't know where to go from here don't have proper calculator or even how to use the online one.
1 answer