Question

PLEASE HELP!!! URGENT

Answer 1

Answer-

The cubic equation-

$f(x)=0.00009121x^3-0.00666099x^2+0.427014x+1.36845$

Milk consumption in 1994 was 58.4 pounds.

Solution-

The general form of a cubic model is,

$f(x)=ax^3+bx^2+cx+d$

x = input variable = year - 2000 i.e number years after 2000

y = output variable = milk consumed in pounds

Then putting the values from the table,

$2.592=a(3)^3+b(3)^2+c(3)+d$

$\Rightarrow 2.592=27a+9b+3c+d$ --------------------------1

$13.301=a(39)^3+b(39)^2+c(39)+d$

$\Rightarrow 13.301=59319a+1521b+39c+d$ -------------2

$20.41=a(56)^3+b(56)^2+c(56)+d$

$\Rightarrow 20.41=175616a+3136b+56c+d$ -------------3

$63.359=a(97)^3+b(97)^2+c(97)+d$

$\Rightarrow 63.359=912673a+9409b+97c+d$ ------------4

Solving equations (1), (2), (3) and (4) simultaneously we get,

$a=0.00009121,\\\\b=-0.00666099,\\\\c=0.427014,\\\\d=1.36845$

So, the equation becomes,

$f(x)=0.00009121x^3-0.00666099x^2+0.427014x+1.36845$

In order to get the milk consumption in 1994, putting x=94

$=0.00009121(94)^3-0.00666099(94)^2+0.427014(94)+1.36845$

$=(0.00009121)\cdot (830584)-(0.00666099)\cdot (8836)+(0.427014)\cdot (94)+(1.36845)$

$=58.4088$

Therefore, milk consumption in 1994 was 58.4 pounds.