that the world's current oil reserves is R= 1870 billion barrels. If, on average, the total Suppose reserves is decreasing by 23 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.
![### Analysis of Depleting Oil Reserves
#### Problem Statement:
Suppose that the world's current oil reserves is \( R = 1870 \) billion barrels. If, on average, the total reserves are decreasing by 23 billion barrels of oil each year, answer the following:
#### A. Linear Equation for Total Remaining Oil Reserves
**Question:** 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.)
**Response:**
\[ R = \]
#### B. Future Oil Reserves Estimation
**Question:** 5 years from now, the total oil reserves will be \( \_\_\_\_ \) billions of barrels.
**Response:**
\[ \]
#### C. Complete Depletion Estimation
**Question:** 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.)
**Response:**
\[ \]
### Explanation:
1. **Equation for Remaining Oil Reserves:**
The depletion rate of the oil reserves is provided as 23 billion barrels per year. Given the current reserves are 1870 billion barrels, the reserves diminish over time linearly. The generic linear equation for this situation, where \( t \) represents the number of years since now, can be represented as:
\[
R = 1870 - 23t
\]
2. **Reserves After 5 Years:**
To find the reserves after 5 years, substitute \( t = 5 \) into the linear equation derived in Part A:
\[
R = 1870 - 23 \times 5 = 1870 - 115 = 1755 \text{ billion barrels}
\]
3. **Year of Complete Depletion:**
To find when the reserves will be completely depleted, set \( R = 0 \):
\[
0 = 1870 - 23t \implies 23t = 1870 \implies t = \frac{1870}{23} \approx 81.30 \text{ years}
\]
This signifies that the oil reserves will be depleted approximately 81.30 years](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88d18a19-21f4-41fb-afe0-306734676977%2Fdde2a7fb-0fc4-451b-b40e-4ef11d685714%2Ff3rpjcm.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
