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, $R,$ 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 the world'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, $R,$ 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 the world's oil reserves be
depleted?

Key Concepts

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.

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.

Transcript

00:01 Okay, so in this question, we are given the total number of the world's oil reserves as of 2014, and the rate at which is decreasing.

00:13 We are asked to find a linear equation for the remaining oil reserves are in terms of t, which is the time.

00:23 We also ask to calculate for what we left seven years from now.

00:28 So to solve this question, you need an in -depth knowledge in linear modeling.

00:33 And the basic key to understanding everything about this question is to understand the equation of a line, the general equation of a line, which is given us y is equal to mx plus c, where m is the gradient.

00:52 Most formula is changing y over changing x.

00:57 That's popularly known as rise overrun the c is the y intersect that is the value of why when x is equal to zero that's clearly known as if i place zero here when x equals zero y is equal to c so in this question you are told as of 2014 in this question sorry let me tell you once again we are using x to be t because that's what they asked us to use and r is y so we're writing this general equation we have r to be equal to m t plus c so that's a general linear equation for this particular question we are yet to simplify it and input the values that we were given so paying critical look at it's decided in 2014 the oil reserve was 1 ,820 barrels as of 2014 so in 2014 t was equal to zero because that's the initial year that will be given so if t is equal to zero going back to this place we are told that t which used to be x when it's equal to zero any value that you be given is the what is the c also known as the y intercept so when t is equal to zero, there are 1 ,100 ,000 ,000 ,000, 820 barrels, 1 ,820 billion barrels of oil as of 2014.

02:56 So that's our y intercept...

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