Question

Suppose that the world's current oil reserves is R = 1820 billion barrels. If, on average, the total reserves

is decreasing by 18 billion barrels of oil each year, answer the following:
A.) Give a linear equation for the total remaining oil reserves, R, in billions of barrels, in terms of t, the
number of years since now. (Be sure to use the correct variable and Preview before you submit.)
R
B.) 14 years from now, the total oil reserves will be
billions of barrels.
C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all
used up) approximately
years from now.
(Round your answer to two decimal places.)

Answer 1

A. R = -18t + 1,820

B. 1,568 billions of barrels

C. approximately 101.11 years

Explanation:

To make our equation, we'll use the form R = mt + b. M represents how many billion barrels of oil are being lost each year, which we know is 18 billion. So -18 will be our m. B is how many total barrels of oil there are, which is 1,820. So 1,820 will be our b. Now the equation looks like this:

R = -18t + 1,820

We can use this equation to answer Part B.

Replace the t with 14:

R = -18(14) + 1,820

Now solve for R:

R = -18(14) + 1,820

R = -252 + 1,820

R = 1,568

14 years from now, there will be 1,568 billions of barrels left.

To solve part C, we need to find how many years it will take for all of the oil to be used up. After it's all used up, the total amount of oil will be 0, so we can replace R with 0 and then solve for t:

0 = -18t + 1,820

Subtract 1,820 from both sides to isolate -18t:

0 - 1,820 = -18t + 1,820 - 1,820

-1,820 = -18t

Divide both sides by -18 to isolate the t:

-1,820/-18 = -18t/-18

101.11 = t

After approximately 101.11 years, all of the oil will be used up.