Suppose that the world's current oil reserves is $R=1890$ 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.) 7 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.)
Solution
Step 1 ：Suppose that the world's current oil reserves is \(R=1890\) billion barrels. If, on average, the total reserves is decreasing by 18 billion barrels of oil each year, we are asked to find a linear equation for the total remaining oil reserves, \(R\), in billions of barrels, in terms of \(t\), the number of years since now.
Step 2 ：The initial amount of oil is 1890 billion barrels and it decreases by 18 billion barrels each year. This can be represented by the equation \(R = 1890 - 18t\), where \(R\) is the remaining oil reserves and \(t\) is the time in years.
Step 3 ：Final Answer: The linear equation for the total remaining oil reserves, \(R\), in billions of barrels, in terms of \(t\), the number of years since now is \(\boxed{R = 1890 - 18t}\)
