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Algebra / Linear functions Difficulty: Hard

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?

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Explanation

Choice C is correct. 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, $f of t equals, m, t plus b$ , 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, $b equals 4$ . The rate of change, m, can be calculated as $the fraction with numerator 4 minus 1 point 9, and denominator 0 minus 13, end fraction, equals, the negative of the fraction 2 point 1 over 13$ , which is equivalent to $the negative of the fraction 21 over 130$ , 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.