Questions: Suppose that the world's current oil reserves is R=1830 billion barrels. total reserves is decreasing by 25 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.) 13 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.)

Suppose that the world's current oil reserves is R=1830 billion barrels. total reserves is decreasing by 25 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.) 13 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.)
Transcript text: Suppose that the world's current oil reserves is $R=1830$ billion barrels. total reserves is decreasing by 25 billion barrels of oil each year, answer the following: A.) Give a linear equation for the total remainin̄g 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.) $R=$ $\square$ B.) 13 years from now, the total oil reserves will be $\square$ 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 $\square$ years from now. (Round your answer to two decimal places.)
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Solution

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Solution Steps

Step 1: Determine the Initial Quantity of the Resource

The initial quantity of the resource, $R_0$, is given as 1830.

Step 2: Determine the Rate of Depletion

The rate of depletion, $d$, is given as 25 per unit time.

Step 3: Calculate the Remaining Quantity of the Resource

Using the formula $R = R_0 - d \cdot t$, where $t$ is 13, we find the remaining quantity of the resource, $R$, to be 1505.

Step 4: Calculate the Time When the Resource Will Be Completely Depleted

Setting $R = 0$ and solving for $t$ gives $t = \frac{R_0}{d} = 73.2$.

Final Answer

The remaining quantity of the resource at time 13 is 1505, and it will be completely depleted in 73.2 units of time (if $d > 0$).

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