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?
Correct answer: C. f(t) = (-21/130)t + 4
- 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
Explanation
The correct answer is Option C: f(t) = (-21/130)t + 4. The production of oil and gas decreased from 4 million barrels in 2000 to 1.9 million barrels in 2013, a period of 13 years. The initial value of 4 represents the production level in 2000, and the negative rate of change, -21/130, represents the annual decrease in production. This linear function accurately models the situation described in the question.Options A and B are incorrect because they propose a positive rate of change, which does not align with the given scenario of decreasing production. Option D miscalculates the rate of change, assuming a smaller decrease than actually occurred.
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