Which Expression Describes The Gallons Of Gas In The Tank After D D D Days?A. 14 − 0.5 D 14 - 0.5d 14 − 0.5 D B. 14 D − 0.5 14d - 0.5 14 D − 0.5 C. 0.5 − 14 D 0.5 - 14d 0.5 − 14 D D. 0.5 D − 14 0.5d - 14 0.5 D − 14

Introduction

In this article, we will explore the concept of gas tank capacity over time. We will examine a scenario where a gas tank initially contains a certain amount of gas, and we need to determine the expression that describes the gallons of gas in the tank after a certain number of days. This problem involves understanding the relationship between the initial amount of gas, the rate at which gas is consumed, and the time elapsed.

The Problem

A car's gas tank initially contains 14 gallons of gas. The car consumes gas at a rate of 0.5 gallons per day. We need to find the expression that describes the gallons of gas in the tank after d days.

Analyzing the Options

Let's analyze each option to determine which one accurately describes the gallons of gas in the tank after d days.

Option A: $14 - 0.5d$

This option suggests that the amount of gas in the tank decreases by 0.5 gallons each day. However, this is not accurate because the initial amount of gas is 14 gallons, and the rate of consumption is 0.5 gallons per day. Therefore, the amount of gas in the tank will decrease by 0.5 gallons each day, but the initial amount of gas will remain the same.

Option B: $14d - 0.5$

This option suggests that the amount of gas in the tank increases by 14 gallons each day and then decreases by 0.5 gallons. However, this is not accurate because the initial amount of gas is 14 gallons, and the rate of consumption is 0.5 gallons per day. Therefore, the amount of gas in the tank will decrease by 0.5 gallons each day, not increase.

Option C: $0.5 - 14d$

This option suggests that the amount of gas in the tank decreases by 14 gallons each day and then increases by 0.5 gallons. However, this is not accurate because the initial amount of gas is 14 gallons, and the rate of consumption is 0.5 gallons per day. Therefore, the amount of gas in the tank will decrease by 0.5 gallons each day, not increase.

Option D: $0.5d - 14$

This option suggests that the amount of gas in the tank decreases by 0.5 gallons each day and then subtracts 14 gallons. However, this is not accurate because the initial amount of gas is 14 gallons, and the rate of consumption is 0.5 gallons per day. Therefore, the amount of gas in the tank will decrease by 0.5 gallons each day, and the initial amount of gas will remain the same.

The Correct Answer

Based on the analysis above, the correct answer is Option A: $14 - 0.5d$. This option accurately describes the gallons of gas in the tank after d days. The initial amount of gas is 14 gallons, and the rate of consumption is 0.5 gallons per day. Therefore, the amount of gas in the tank will decrease by 0.5 gallons each day, and the expression $14 - 0.5d$ accurately describes this relationship.

Conclusion

In conclusion, the expression that describes the gallons of gas in the tank after d days is $14 - 0.5d$. This expression accurately takes into account the initial amount of gas and the rate of consumption. By understanding the relationship between the initial amount of gas, the rate of consumption, and the time elapsed, we can determine the correct expression that describes the gallons of gas in the tank after d days.

Mathematical Representation

The mathematical representation of the problem can be expressed as:

Let G(d) be the amount of gas in the tank after d days.

G(d) = 14 - 0.5d

This equation accurately describes the relationship between the initial amount of gas, the rate of consumption, and the time elapsed.

Real-World Applications

This problem has real-world applications in various fields, such as:

• Transportation: Understanding the relationship between the initial amount of gas, the rate of consumption, and the time elapsed is crucial in transportation planning and logistics.
• Energy Management: Accurately determining the amount of gas in the tank after a certain number of days is essential in energy management and resource allocation.
• Environmental Science: Understanding the relationship between the initial amount of gas, the rate of consumption, and the time elapsed is crucial in environmental science and sustainability planning.

Conclusion

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Frequently Asked Questions

In this article, we will address some of the most frequently asked questions related to gas tank capacity over time.

Q: What is the initial amount of gas in the tank?

A: The initial amount of gas in the tank is 14 gallons.

Q: What is the rate of gas consumption?

A: The rate of gas consumption is 0.5 gallons per day.

Q: How can I determine the amount of gas in the tank after d days?

A: To determine the amount of gas in the tank after d days, you can use the expression $14 - 0.5d$. This expression accurately takes into account the initial amount of gas and the rate of consumption.

Q: What happens to the amount of gas in the tank over time?

A: The amount of gas in the tank decreases over time due to the rate of consumption. The expression $14 - 0.5d$ accurately describes this relationship.

Q: Can I use the expression $14d - 0.5$ to determine the amount of gas in the tank after d days?

A: No, you cannot use the expression $14d - 0.5$ to determine the amount of gas in the tank after d days. This expression is incorrect and does not accurately take into account the initial amount of gas and the rate of consumption.

Q: Can I use the expression $0.5 - 14d$ to determine the amount of gas in the tank after d days?

A: No, you cannot use the expression $0.5 - 14d$ to determine the amount of gas in the tank after d days. This expression is incorrect and does not accurately take into account the initial amount of gas and the rate of consumption.

Q: Can I use the expression $0.5d - 14$ to determine the amount of gas in the tank after d days?

A: No, you cannot use the expression $0.5d - 14$ to determine the amount of gas in the tank after d days. This expression is incorrect and does not accurately take into account the initial amount of gas and the rate of consumption.

Q: What is the correct expression to use to determine the amount of gas in the tank after d days?

A: The correct expression to use to determine the amount of gas in the tank after d days is $14 - 0.5d$.

Q: Why is it important to understand the relationship between the initial amount of gas, the rate of consumption, and the time elapsed?

A: It is essential to understand the relationship between the initial amount of gas, the rate of consumption, and the time elapsed to accurately determine the amount of gas in the tank after a certain number of days. This understanding is crucial in various fields, such as transportation, energy management, and environmental science.

Conclusion

In conclusion, understanding gas tank capacity over time is crucial in various fields. By using the correct expression $14 - 0.5d$, you can accurately determine the amount of gas in the tank after a certain number of days. We hope this Q&A article has provided you with a better understanding of the topic.

Additional Resources

For more information on gas tank capacity over time, please refer to the following resources:

• Mathematical Representation: The mathematical representation of the problem can be expressed as: G(d) = 14 - 0.5d
• Real-World Applications: Understanding the relationship between the initial amount of gas, the rate of consumption, and the time elapsed is crucial in transportation planning and logistics, energy management, and environmental science.
• Frequently Asked Questions: We have addressed some of the most frequently asked questions related to gas tank capacity over time in this article.