Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year 2000?

Options

A. `f(t)=21/130 t+4`
B. `f(t)=19/130 t+4`
C. `f(t) =-21/130 t+4`
D. `f(t)=-19/130 t+4`

Answer

C

Explanation

It is assumed that the oil and gas production decreased at a constant rate. Therefore, the function f that best models the production t years after the year 2000 can be written as a linear function, f (t) = mt + b, where m is the rate of change of the oil and gas production and b is the oil and gas production, in millions of barrels, in the year 2000. Since there were 4 million barrels of oil and gas produced in 2000, b = 4. The rate of change, m, can be calculated as `(4-1.9)/(0-13)=-2.1/13`, which is equivalent to `-21/130` , the rate of change in choice C.
Choices A and B are incorrect because each of these functions has a positive rate of change. Since the oil and gas production decreased over time, the rate of change must be negative. Choice D is incorrect. This model may result from misinterpreting 1.9 million barrels as the amount by which the production decreased.