I am stuck!

Question

Polynomial 0.0011x^3-0.07x^2+11 models natural gas consumption in trillions of cubic feet, where x=0 corresponds to 1960, x=1 to 1961, and so on, in  which year between 1970 and 1990 was natural gas about 26.5 trillion cubic ft.?

Answer 1

0.0011x^3-0.07x^2+11=26.5 will give an x value for gas consumption as one of its solutions.

0.0011x^3-0.07x^2-15.5=0. The only real solution is when x=66.8 which corresponds to 1960+66.8=2027 approx!

This suggests that the polynomial has not been correctly presented (a missing term?).

In 1960, x=0 and gas consumption is 11 trillion cu ft.

In 1961, x=1 and consumption is about 11.0011-0.07=10.931 (lower than 1960).

By 1970 (x=10) consumption drops to 5.1 and by 1974 it is about 0.3. By 1975 it's zero. So this points to a missing x term. I suggest the missing term is something like 1.75x. So we would need to solve:

0.0011x^3-0.07x^2+1.75x-15.5=0. This gives us x=19 approximately corresponding to 1960+19=1979 when natural gas consumption reaches 26.5 trillion cu ft.