Suppose the world's oil reserves in 2014 are 1,820 billion...

Suppose the world's oil reserves in 2014 are $1,820$ billion barrels. If, on average, the total reserves are decreasing by 25 billion barrels of oil each year: a. Give a linear equation for the remaining oil reserves, $\mathrm{R}$ , 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 at which the reserves are decreasing is constant, when will's oil reserves be depleted?

Suppose the world's oil reserves in 2014 are $1,820$ billion barrels. If, on average, the total reserves are decreasing by 25 billion barrels of oil each year:

a. Give a linear equation for the remaining oil reserves, $\mathrm{R}$ , 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 at which the reserves are decreasing is constant, when will's oil reserves be depleted?

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Key Concepts

Solving Linear Equations

Solving linear equations involves finding the value of the independent variable that satisfies the equation, such as determining when the modeled quantity reaches a specific value (e.g., zero depletion). This process is integral in planning and forecasting, as it allows for the determination of key points in the timeline of the model.

Linear Functions

A linear function provides a model for relationships where one quantity changes at a constant rate with respect to another. In scenarios like modeling resource depletion or growth, the linear function takes the form R(t) = mt + b, where m is the slope representing the rate of change and b is the initial amount.

Slope (Rate of Change)

The slope in a linear function represents the rate at which the dependent variable changes per unit change in the independent variable. In the context of resource depletion, the slope indicates how much the resource amount is decreasing (or increasing) per time period, which is crucial for predicting future levels.

Y-intercept (Initial Value)

The y-intercept in a linear function represents the initial value of the dependent variable when the independent variable is zero. This concept is essential for modeling situations where the starting amount is known, and all future calculations are based on this initial condition.

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