Suppose the world's current oil reserves are 1820 billion...

Suppose the world's current oil reserves are 1820 billion barrels. If, on average, the total reserves is decreasing by 25 billion barrels of oil each year: a. Give a linear equation for the remaining oil reserves, $R$, in terms of $t,$ the number of years since now. b. Seven years from now, what will the oil reserves be? c. If the rate of depletion isn't change, when will the world's oil reserves be depleted?

Suppose the world's current oil reserves are 1820 billion barrels. If, on average, the total reserves is decreasing by 25 billion barrels of oil each year:
a. Give a linear equation for the remaining oil reserves, $R$, in terms of $t,$ the number of years since now.
b. Seven years from now, what will the oil reserves be?
c. If the rate of depletion isn't change, when will the world's oil reserves be depleted?

Key Concepts

Y-intercept Interpretation

The y-intercept in a linear equation represents the initial value of the quantity before any change has occurred. In real-world applications, it provides the baseline from which future predictions are made. Recognizing the y-intercept is crucial, as it sets the starting point for any analysis involving linear trends.

Linear Function Modeling

This concept involves constructing a mathematical model that represents a linear relationship between two variables. In applied contexts, such models are used to predict future values based on a constant rate of change. The general form is R(t) = initial value + (slope × t), where t represents time. This model is essential for understanding how quantities change uniformly over time.

Rate of Change

The rate of change, or slope, in a linear equation indicates how much the dependent variable changes per unit change in the independent variable. In depletion problems, the slope is typically negative, showing a decrease over time. Understanding the rate of change allows one to calculate the decrease or increase in a quantity based on time intervals.

Solving for the Zero Value

This concept involves determining the point at which the value of the dependent variable becomes zero by setting the linear equation equal to zero and solving for the independent variable. It is especially useful in scenarios like resource depletion, as it predicts when a resource will be completely exhausted if the current rate of change remains constant.

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