Select The Correct Answer.The Following Function Describes The Number Of Employees Working At A Company, In Thousands, After The Company Revised The Benefits Package:$f(t)=1.5(0.90)^t$A. The Number Of Employees Is Decreasing By 90% Every

Introduction

In this article, we will delve into the world of mathematics, specifically focusing on a function that describes the number of employees working at a company after a revision in the benefits package. The function, $f(t)=1.5(0.90)^t$, is a classic example of an exponential function, where the number of employees decreases by a certain percentage every time period. In this case, the number of employees decreases by 90% every time period. Our goal is to understand the behavior of this function and select the correct answer based on the given information.

What is an Exponential Function?

An exponential function is a mathematical function that describes a relationship between two variables, where one variable is a constant power of the other variable. In the case of the function $f(t)=1.5(0.90)^t$, the variable $t$ represents the time period, and the constant $1.5$ is the initial number of employees. The exponent $t$ indicates that the number of employees decreases by a certain percentage every time period.

Understanding the Function

To understand the behavior of the function, let's break it down into its components. The function $f(t)=1.5(0.90)^t$ can be rewritten as:

$f(t) = 1.5 \times (0.90)^t$

Where:

• $1.5$ is the initial number of employees
• $(0.90)^t$ represents the decrease in the number of employees by 90% every time period

Interpreting the Function

To interpret the function, let's consider a few examples:

• If $t=0$, the number of employees is $1.5 \times (0.90)^0 = 1.5$
• If $t=1$, the number of employees is $1.5 \times (0.90)^1 = 1.35$
• If $t=2$, the number of employees is $1.5 \times (0.90)^2 = 1.215$
• If $t=3$, the number of employees is $1.5 \times (0.90)^3 = 1.0955$

As we can see, the number of employees decreases by 90% every time period. This is a classic example of an exponential decay function.

Selecting the Correct Answer

Based on the function $f(t)=1.5(0.90)^t$, we can conclude that the number of employees is decreasing by 90% every time period. Therefore, the correct answer is:

A. The number of employees is decreasing by 90% every time period

Conclusion

In conclusion, the function $f(t)=1.5(0.90)^t$ describes the number of employees working at a company after a revision in the benefits package. The function is an example of an exponential decay function, where the number of employees decreases by 90% every time period. By understanding the behavior of this function, we can select the correct answer and gain a deeper understanding of the mathematical concepts involved.

Frequently Asked Questions

Q: What is the initial number of employees?

A: The initial number of employees is 1.5, as indicated by the constant 1.5 in the function.

Q: What is the percentage decrease in the number of employees every time period?

A: The number of employees decreases by 90% every time period, as indicated by the exponent (0.90)^t.

Q: Is the function an example of an exponential growth or decay function?

A: The function is an example of an exponential decay function, where the number of employees decreases by 90% every time period.

Q: How can we interpret the function?

A: We can interpret the function by considering a few examples, such as the number of employees at different time periods.

References

• [1] "Exponential Functions" by Math Open Reference
• [2] "Exponential Decay" by Khan Academy

Glossary

• Exponential function: A mathematical function that describes a relationship between two variables, where one variable is a constant power of the other variable.
• Exponential decay: A type of exponential function where the value decreases by a certain percentage every time period.
• Initial value: The starting value of a function, which in this case is 1.5.
• Exponent: A constant that is raised to a power in an exponential function, which in this case is (0.90)^t.
  Q&A: Understanding the Function and Its Behavior =====================================================

Introduction

In our previous article, we explored the function $f(t)=1.5(0.90)^t$ and its behavior. We learned that the function describes the number of employees working at a company after a revision in the benefits package, and that the number of employees decreases by 90% every time period. In this article, we will answer some frequently asked questions about the function and its behavior.

Q: What is the significance of the constant 1.5 in the function?

A: The constant 1.5 represents the initial number of employees. It is the starting value of the function, and it indicates that there are 1.5 thousand employees at the beginning.

Q: How can we calculate the number of employees at a specific time period?

A: To calculate the number of employees at a specific time period, we can plug in the value of t into the function. For example, if we want to find the number of employees at t=5, we can calculate:

$f(5) = 1.5 \times (0.90)^5$

This will give us the number of employees at t=5.

Q: What happens to the number of employees as time goes on?

A: As time goes on, the number of employees decreases by 90% every time period. This means that the number of employees will continue to decrease exponentially, and it will approach zero as time goes on.

Q: Can we use this function to model other real-world situations?

A: Yes, we can use this function to model other real-world situations where the value decreases by a certain percentage every time period. For example, we can use this function to model the population of a city that is decreasing due to emigration, or the amount of money in a bank account that is decreasing due to withdrawals.

Q: How can we graph this function?

A: We can graph this function by plotting the values of f(t) against the values of t. This will give us a graph that shows the behavior of the function over time.

Q: What is the domain of this function?

A: The domain of this function is all real numbers, since we can plug in any value of t into the function and get a valid result.

Q: What is the range of this function?

A: The range of this function is all real numbers greater than or equal to zero, since the number of employees cannot be negative.

Q: Can we use this function to model other types of decay?

A: Yes, we can use this function to model other types of decay, such as radioactive decay or chemical decay. However, we would need to adjust the function to reflect the specific type of decay we are modeling.

Q: How can we use this function in real-world applications?

A: We can use this function in real-world applications such as:

• Modeling the population of a city that is decreasing due to emigration
• Modeling the amount of money in a bank account that is decreasing due to withdrawals
• Modeling the number of employees in a company that is decreasing due to layoffs
• Modeling the amount of a substance that is decreasing due to chemical reactions

Conclusion

In conclusion, the function $f(t)=1.5(0.90)^t$ is a powerful tool for modeling real-world situations where the value decreases by a certain percentage every time period. By understanding the behavior of this function, we can use it to model a wide range of real-world applications.

Frequently Asked Questions

Q: What is the significance of the exponent (0.90)^t in the function?

A: The exponent (0.90)^t represents the decrease in the number of employees by 90% every time period.

Q: Can we use this function to model other types of growth?

A: No, this function is specifically designed to model exponential decay, not growth.

Q: How can we adjust the function to model other types of decay?

A: We can adjust the function by changing the value of the exponent or the initial value.

Q: Can we use this function to model other real-world situations?

A: Yes, we can use this function to model other real-world situations where the value decreases by a certain percentage every time period.

References

• [1] "Exponential Functions" by Math Open Reference
• [2] "Exponential Decay" by Khan Academy

Glossary

• Exponential function: A mathematical function that describes a relationship between two variables, where one variable is a constant power of the other variable.
• Exponential decay: A type of exponential function where the value decreases by a certain percentage every time period.
• Initial value: The starting value of a function, which in this case is 1.5.
• Exponent: A constant that is raised to a power in an exponential function, which in this case is (0.90)^t.