PLEASE HELP!!! URGENT The table shows the annual consumption of cheese per person in the U.S. for selected years in the 20th century. Use a cubic model to estimate milk producti…

Question

asked Jul 26, 2019 225k views

1 Answer

Jeff Dallien · Answer 1 · 2019-07-30T08:58:50+0000

Answer-

The cubic equation-

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.