Oil and gas production in a certain area dropped from 4...

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$?$ A) $f(t)=\frac{21}{130} t+4$ B) $f(t)=\frac{19}{130} t+4$ C) $f(t)=-\frac{21}{130} t+4$ D) $f(t)=-\frac{19}{130} t+4$

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$?$
A) $f(t)=\frac{21}{130} t+4$
B) $f(t)=\frac{19}{130} t+4$
C) $f(t)=-\frac{21}{130} t+4$
D) $f(t)=-\frac{19}{130} t+4$

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Key Concepts

Linear Functions

A linear function is a mathematical representation where the change between any two values is constant, resulting in a straight-line graph. In real-world modeling, such as production levels over time, a linear function is used to predict values based on an established rate of change, using the formula f(t) = mt + b.

Slope

The slope of a linear function represents the rate of change, indicating how much the dependent variable changes for each unit increase in the independent variable. When modeling changes over time, such as a decrease in production, the slope is calculated as the difference in production values divided by the difference in time.

Y-intercept

The y-intercept in a linear function is the value when the independent variable is zero. In time-based models, it typically represents the initial condition or starting value at the beginning of the time period being considered, which helps ground the model in actual data.

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