The Sequence $a_n=12,000-200n$ Represents The Number Of Gallons Of Diesel Fuel Remaining In A Fuel Station's Tank After $n$ Semi-truck Owners Have Filled Their Tanks. If $1 \leq N \leq 7$, Which Table Represents The

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Introduction

In this article, we will explore the sequence $a_n=12,000-200n$, which represents the number of gallons of diesel fuel remaining in a fuel station's tank after $n$ semi-truck owners have filled their tanks. We will examine the sequence for the values of $n$ ranging from 1 to 7 and create a table to represent the number of gallons of diesel fuel remaining in the tank after each semi-truck owner has filled their tank.

Understanding the Sequence

The sequence $a_n=12,000-200n$ is a linear sequence, where each term is obtained by subtracting 200 from the previous term. The first term of the sequence is 12,000, which represents the initial amount of diesel fuel in the tank. As each semi-truck owner fills their tank, the amount of diesel fuel remaining in the tank decreases by 200 gallons.

Calculating the Number of Gallons of Diesel Fuel Remaining

To calculate the number of gallons of diesel fuel remaining in the tank after each semi-truck owner has filled their tank, we can plug in the values of $n$ into the sequence $a_n=12,000-200n$.

For n = 1

When $n=1$, the number of gallons of diesel fuel remaining in the tank is:

a1=12,000−200(1)=12,000−200=11,800a_1=12,000-200(1)=12,000-200=11,800

For n = 2

When $n=2$, the number of gallons of diesel fuel remaining in the tank is:

a2=12,000−200(2)=12,000−400=11,600a_2=12,000-200(2)=12,000-400=11,600

For n = 3

When $n=3$, the number of gallons of diesel fuel remaining in the tank is:

a3=12,000−200(3)=12,000−600=11,400a_3=12,000-200(3)=12,000-600=11,400

For n = 4

When $n=4$, the number of gallons of diesel fuel remaining in the tank is:

a4=12,000−200(4)=12,000−800=11,200a_4=12,000-200(4)=12,000-800=11,200

For n = 5

When $n=5$, the number of gallons of diesel fuel remaining in the tank is:

a5=12,000−200(5)=12,000−1000=11,000a_5=12,000-200(5)=12,000-1000=11,000

For n = 6

When $n=6$, the number of gallons of diesel fuel remaining in the tank is:

a6=12,000−200(6)=12,000−1200=10,800a_6=12,000-200(6)=12,000-1200=10,800

For n = 7

When $n=7$, the number of gallons of diesel fuel remaining in the tank is:

a7=12,000−200(7)=12,000−1400=10,600a_7=12,000-200(7)=12,000-1400=10,600

Creating a Table to Represent the Sequence

Based on the calculations above, we can create a table to represent the number of gallons of diesel fuel remaining in the tank after each semi-truck owner has filled their tank.

n Number of Gallons of Diesel Fuel Remaining
1 11,800
2 11,600
3 11,400
4 11,200
5 11,000
6 10,800
7 10,600

Conclusion

In this article, we explored the sequence $a_n=12,000-200n$, which represents the number of gallons of diesel fuel remaining in a fuel station's tank after $n$ semi-truck owners have filled their tanks. We calculated the number of gallons of diesel fuel remaining in the tank after each semi-truck owner has filled their tank and created a table to represent the sequence. This table can be used to determine the number of gallons of diesel fuel remaining in the tank after a certain number of semi-truck owners have filled their tanks.

Recommendations

Based on the calculations above, we can make the following recommendations:

  • The fuel station should have a minimum of 10,600 gallons of diesel fuel in the tank to ensure that there is enough fuel for all semi-truck owners.
  • The fuel station should consider increasing the size of the tank to accommodate more semi-truck owners.
  • The fuel station should consider implementing a system to track the amount of diesel fuel remaining in the tank in real-time.

Future Research Directions

Based on the calculations above, we can identify the following future research directions:

  • Investigating the impact of different tank sizes on the amount of diesel fuel remaining in the tank.
  • Developing a system to track the amount of diesel fuel remaining in the tank in real-time.
  • Investigating the impact of different semi-truck owner behaviors on the amount of diesel fuel remaining in the tank.
    Frequently Asked Questions (FAQs) about the Sequence of Diesel Fuel Remaining in a Fuel Station's Tank =============================================================================================

Q: What is the sequence $a_n=12,000-200n$?

A: The sequence $a_n=12,000-200n$ represents the number of gallons of diesel fuel remaining in a fuel station's tank after $n$ semi-truck owners have filled their tanks.

Q: How is the sequence calculated?

A: The sequence is calculated by subtracting 200 from the previous term. The first term of the sequence is 12,000, which represents the initial amount of diesel fuel in the tank.

Q: What is the significance of the sequence?

A: The sequence is significant because it helps to determine the number of gallons of diesel fuel remaining in the tank after a certain number of semi-truck owners have filled their tanks.

Q: How can the sequence be used in real-world applications?

A: The sequence can be used in real-world applications such as:

  • Determining the amount of diesel fuel remaining in a fuel station's tank after a certain number of semi-truck owners have filled their tanks.
  • Planning for fuel deliveries to ensure that the fuel station has enough diesel fuel to meet the demands of semi-truck owners.
  • Developing strategies to reduce fuel consumption and minimize waste.

Q: What are some potential limitations of the sequence?

A: Some potential limitations of the sequence include:

  • The sequence assumes that each semi-truck owner fills their tank with the same amount of diesel fuel.
  • The sequence does not take into account factors such as fuel efficiency, traffic patterns, and weather conditions that can affect fuel consumption.

Q: How can the sequence be modified to account for these limitations?

A: The sequence can be modified to account for these limitations by:

  • Incorporating additional variables that take into account factors such as fuel efficiency, traffic patterns, and weather conditions.
  • Using more complex mathematical models that can capture the nuances of real-world fuel consumption.

Q: What are some potential future research directions related to the sequence?

A: Some potential future research directions related to the sequence include:

  • Investigating the impact of different tank sizes on the amount of diesel fuel remaining in the tank.
  • Developing a system to track the amount of diesel fuel remaining in the tank in real-time.
  • Investigating the impact of different semi-truck owner behaviors on the amount of diesel fuel remaining in the tank.

Q: How can the sequence be used to inform business decisions?

A: The sequence can be used to inform business decisions such as:

  • Determining the optimal size of the fuel tank to meet the demands of semi-truck owners.
  • Developing strategies to reduce fuel consumption and minimize waste.
  • Planning for fuel deliveries to ensure that the fuel station has enough diesel fuel to meet the demands of semi-truck owners.

Q: What are some potential benefits of using the sequence in business decision-making?

A: Some potential benefits of using the sequence in business decision-making include:

  • Improved fuel efficiency and reduced waste.
  • Increased customer satisfaction due to reduced wait times and improved fuel availability.
  • Enhanced competitiveness in the market due to improved fuel management and reduced costs.

Q: How can the sequence be used to inform policy decisions?

A: The sequence can be used to inform policy decisions such as:

  • Developing regulations to ensure that fuel stations have adequate fuel supplies to meet the demands of semi-truck owners.
  • Implementing policies to reduce fuel consumption and minimize waste.
  • Developing strategies to promote fuel efficiency and reduce emissions.

Q: What are some potential benefits of using the sequence in policy decision-making?

A: Some potential benefits of using the sequence in policy decision-making include:

  • Improved fuel efficiency and reduced waste.
  • Increased customer satisfaction due to reduced wait times and improved fuel availability.
  • Enhanced competitiveness in the market due to improved fuel management and reduced costs.