Question

suppose that the worlds current oil reserves is (r = 1890) billion barrels. if, on average, the total reserves is decreasing by 21 billion barrels of oil each year, answer the following:

a.) give a linear equation for the total remaining oil reserves, (r), in terms of (t), the number of years since now. (be sure to use the correct variable and preview before you submit.)

(r =)

b.) 8 years from now, the total oil reserves will be billions of barrels.

c.) if no other oil is deposited into the reserves, the worlds oil reserves will be completely depleted (all used up) approximately years from now.
(round your answer to two decimal places.)

Explanation:

⚡ Using what you learned: Creating Equations to Model Relationships

Step 1: Write the linear equation

The initial oil reserves are \( 1890 \) billion barrels. The reserves decrease by \( 21 \) billion barrels each year.

$$ R = 1890 - 21t $$

Step 2: Calculate reserves after 8 years

Substitute \( t = 8 \) into the equation:

$$ R = 1890 - 21(8) $$

$$ R = 1890 - 168 $$

$$ R = 1722 $$

Step 3: Find when reserves are completely depleted

Set \( R = 0 \) and solve for \( t \):

$$ 0 = 1890 - 21t $$

$$ 21t = 1890 $$

$$ t = \frac{1890}{21} $$

$$ t = 90 $$

Answer:

A.) \( R = 1890 - 21t \)

B.) \( 1722 \)

C.) \( 90 \)