Final answer:
The recurrence relation for the natural gas consumption in New Jersey is C(n) = C(0) * (1 + r)^n. The growth rate can be solved using the formula r = (C(n) / C(0))^(1/n) - 1. The consumption in 2020 will be approximately 842,520 million cubic feet.
Step-by-step explanation:
The recurrence relation for the natural gas consumption in the state of New Jersey is:
C(n) = C(0) * (1 + r)^n
Where C(n) represents the consumption in year n, C(0) represents the initial consumption in 2008, and r represents the growth rate.
To solve the relation in terms of r, we can use the formula:
r = (C(n) / C(0))^(1/n) - 1
Using the given data, we can substitute the values into the formula to compute r:
r = (653,549 / 614,908)^(1/2) - 1
Rounding to four decimal places, r is approximately 0.0311.
To find the consumption in 2020, we can substitute the values into the recurrence relation:
C(12) = 614,908 * (1 + 0.0311)^12
Rounding to the nearest whole number, the consumption in 2020 will be approximately 842,520 million cubic feet.