Suppose that the world's current oil reserves is R = 2200 billion barrels. If, on average, the total reserves is decreasing by 21 billion barrels of oil each year, answer the following:
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### World Oil Reserves Problem
**Context:**
Suppose that the world's current oil reserves are \( R = 2200 \) billion barrels. If, on average, the total reserves are decreasing by 21 billion barrels of oil each year, answer the following:
**A.) Linear Equation for Remaining Oil Reserves:**
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.) Oil Reserves in 12 Years:**
In 12 years from now, the total oil reserves will be \_\_\_\_\_ billions of barrels.
**C.) Total Depletion Time:**
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.)
**Additional Resources:**
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The given problem involves finding a linear equation to describe the depletion of the oil reserves, estimating future reserves, and calculating the time until complete depletion under the given rate of consumption.
To solve:
**1. Finding the linear equation:**
- **Given Data:**
- Current oil reserves: \( R = 2200 \) billion barrels
- Rate of decrease: 21 billion barrels per year
- **Linear Model:**
The linear relationship can be described by:
\[ R = 2200 - 21t \]
where \( t \) is the number of years from now.
**2. Calculating Reserves in 12 Years:**
Plug \( t = 12 \) years into the equation found in Part A:
\[ R = 2200 - 21 \times 12 \]
\[ R = 2200 - 252 \]
\[ R = 1948 \]
So, in 12 years, the oil reserves will be 1948 billion barrels.
**3. Finding Total Depletion Time:**
Set \( R \) to zero and solve for \( t \):
\[ 0 = 2200 - 21t \]
\[ 21t = 2200 \]
\[ t \approx 104.76 \]
Hence, the reserves will be completely depleted](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6010960e-f970-4bb2-b167-12f0ced798a6%2F36cea7fe-faeb-4fd5-8842-5e1e1e706f1d%2F4iz1k9.png&w=3840&q=75)
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