Suppose that the world's current oil reserves is R = 2190 billion barrels. If, on average, the total reserves is decreasing by 22 billion barrels of oil each year, answer the following:

Question

Suppose that the world's current oil reserves is  billion barrels. If, on average, the total reserves is decreasing by  billion barrels of oil each year, answer the following:

A.) Give a linear equation for the total remaining oil reserves, , in terms of the number of years since now.

B.)  years from now, the total oil reserves will be  

C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted approximately  

Answer 1

Hello, Sara,

The rate at which the oil reserves is declining is a constant 22 Billions of Barrels per year (BB/Y), so let's assume this is a linear equation. There is a constant rate of decline so the line depicting the amount remaining should be straight. The best place to start is y = mx + b.

Let's say Y is the amount of oil remaining in Billion Barrels of Oil (BB), X is the time in years, and b is the amount we start with. m in this equation is the slope, or rate of decline in the oil. This is -22 BB/Y. We are starting with 2190 Billion Barrels (BB), so this will be the b, or slope intercept (where T = 0, starting now when we have 2190 BB remaining). Put this together and we arrive at this equation:

Y (BB) = -22 BBY*X + 2190 BB

[The oil remaining is equal to years times the usage plus the oil present at the start at T = 0]

Try it out for values you know or can predict:

This works for X = 0, since Y = 2190BB, the start.

After 1 year, we'd expect to have drawn down 22BB: Y = (-22 BB/Y)*1year + 2190BB; Y = 2168BB, which is correct

Try other years to check this equation.

Then let's use 7 years:

Y = -22*7 + 2190

Y = 2036BB remaining.

Now let's assign a value of "0" to Y and solve for X to find out how many years until the reserves are depleted (Y = 0).

0 = -22X + 2190

-2190 = -22X

X = -2190/-22

X = 95.545 years

Since we only have 2 sig figs, this technically should be rounded to 96 years.

I hope this helps,

Bob