Select The Correct Answer From Each Drop-down Menu.The Function Below Describes The Population Of Caribou In A Tundra, Where $f(t$\] Represents The Number Of Caribou, In Hundreds, And $t$ Represents The Time, In

Introduction

The function $f(t) = 200 - 100\cos(\frac{\pi}{4}t)$ represents the population of caribou in a tundra, where $f(t)$ is the number of caribou, in hundreds, and $t$ is the time, in years. This function describes the oscillating nature of the caribou population over time. In this article, we will explore the given function and use it to answer a series of questions.

The Function

The given function is $f(t) = 200 - 100\cos(\frac{\pi}{4}t)$. This function represents the population of caribou in the tundra. The function has a maximum value of 300 and a minimum value of 100. The function oscillates between these two values, with the amplitude of the oscillation being 100.

Understanding the Oscillation

The function $f(t) = 200 - 100\cos(\frac{\pi}{4}t)$ represents a sinusoidal function, which oscillates between its maximum and minimum values. The amplitude of the oscillation is 100, which means that the population of caribou will vary between 300 and 100. The frequency of the oscillation is determined by the coefficient of $t$ in the cosine function, which is $\frac{\pi}{4}$.

Selecting the Correct Answer

To select the correct answer from each drop-down menu, we need to analyze the given function and the questions that follow. We will use the function to answer each question and select the correct answer from the drop-down menu.

Question 1: What is the maximum value of the caribou population?

• A) 100
• B) 200
• C) 300
• D) 400

The maximum value of the caribou population is 300, which is the value of the function when $\cos(\frac{\pi}{4}t) = -1$. Therefore, the correct answer is:

C) 300

Question 2: What is the minimum value of the caribou population?

• A) 100
• B) 200
• C) 300
• D) 400

The minimum value of the caribou population is 100, which is the value of the function when $\cos(\frac{\pi}{4}t) = 1$. Therefore, the correct answer is:

A) 100

Question 3: What is the amplitude of the oscillation?

• A) 50
• B) 100
• C) 150
• D) 200

The amplitude of the oscillation is 100, which is the difference between the maximum and minimum values of the function. Therefore, the correct answer is:

B) 100

Question 4: What is the frequency of the oscillation?

• A) $\frac{\pi}{2}$
• B) $\frac{\pi}{4}$
• C) $\pi$
• D) $2\pi$

The frequency of the oscillation is determined by the coefficient of $t$ in the cosine function, which is $\frac{\pi}{4}$. Therefore, the correct answer is:

B) $\frac{\pi}{4}$

Question 5: What is the value of the function when $t = 0$?

• A) 100
• B) 200
• C) 300
• D) 400

The value of the function when $t = 0$ is 200, which is the value of the function when $\cos(\frac{\pi}{4}t) = 1$. Therefore, the correct answer is:

B) 200

Question 6: What is the value of the function when $t = 1$?

• A) 100
• B) 200
• C) 300
• D) 400

The value of the function when $t = 1$ is 200, which is the value of the function when $\cos(\frac{\pi}{4}t) = 1$. Therefore, the correct answer is:

B) 200

Question 7: What is the value of the function when $t = 2$?

• A) 100
• B) 200
• C) 300
• D) 400

The value of the function when $t = 2$ is 100, which is the value of the function when $\cos(\frac{\pi}{4}t) = -1$. Therefore, the correct answer is:

A) 100

Question 8: What is the value of the function when $t = 3$?

• A) 100
• B) 200
• C) 300
• D) 400

The value of the function when $t = 3$ is 300, which is the value of the function when $\cos(\frac{\pi}{4}t) = -1$. Therefore, the correct answer is:

C) 300

Question 9: What is the value of the function when $t = 4$?

• A) 100
• B) 200
• C) 300
• D) 400

The value of the function when $t = 4$ is 200, which is the value of the function when $\cos(\frac{\pi}{4}t) = 1$. Therefore, the correct answer is:

B) 200

Question 10: What is the value of the function when $t = 5$?

• A) 100
• B) 200
• C) 300
• D) 400

The value of the function when $t = 5$ is 100, which is the value of the function when $\cos(\frac{\pi}{4}t) = -1$. Therefore, the correct answer is:

A) 100

Conclusion

In this article, we have explored the given function $f(t) = 200 - 100\cos(\frac{\pi}{4}t)$, which represents the population of caribou in a tundra. We have used the function to answer a series of questions and select the correct answer from each drop-down menu. The correct answers are:

• Question 1: C) 300
• Question 2: A) 100
• Question 3: B) 100
• Question 4: B) $\frac{\pi}{4}$
• Question 5: B) 200
• Question 6: B) 200
• Question 7: A) 100
• Question 8: C) 300
• Question 9: B) 200
• Question 10: A) 100

Frequently Asked Questions

Q1: What is the purpose of the caribou population model?

A1: The caribou population model is used to describe the oscillating nature of the caribou population over time. It helps us understand the factors that affect the population and make predictions about future trends.

Q2: What is the maximum value of the caribou population?

A2: The maximum value of the caribou population is 300, which is the value of the function when $\cos(\frac{\pi}{4}t) = -1$.

Q3: What is the minimum value of the caribou population?

A3: The minimum value of the caribou population is 100, which is the value of the function when $\cos(\frac{\pi}{4}t) = 1$.

Q4: What is the amplitude of the oscillation?

A4: The amplitude of the oscillation is 100, which is the difference between the maximum and minimum values of the function.

Q5: What is the frequency of the oscillation?

A5: The frequency of the oscillation is determined by the coefficient of $t$ in the cosine function, which is $\frac{\pi}{4}$.

Q6: What is the value of the function when $t = 0$?

A6: The value of the function when $t = 0$ is 200, which is the value of the function when $\cos(\frac{\pi}{4}t) = 1$.

Q7: What is the value of the function when $t = 1$?

A7: The value of the function when $t = 1$ is 200, which is the value of the function when $\cos(\frac{\pi}{4}t) = 1$.

Q8: What is the value of the function when $t = 2$?

A8: The value of the function when $t = 2$ is 100, which is the value of the function when $\cos(\frac{\pi}{4}t) = -1$.

Q9: What is the value of the function when $t = 3$?

A9: The value of the function when $t = 3$ is 300, which is the value of the function when $\cos(\frac{\pi}{4}t) = -1$.

Q10: What is the value of the function when $t = 4$?

A10: The value of the function when $t = 4$ is 200, which is the value of the function when $\cos(\frac{\pi}{4}t) = 1$.

Q11: What is the value of the function when $t = 5$?

A11: The value of the function when $t = 5$ is 100, which is the value of the function when $\cos(\frac{\pi}{4}t) = -1$.

Q12: How does the caribou population model relate to the real world?

A12: The caribou population model is a mathematical representation of the oscillating nature of the caribou population over time. It can be used to make predictions about future trends and understand the factors that affect the population.

Q13: What are some of the limitations of the caribou population model?

A13: Some of the limitations of the caribou population model include the assumption of a sinusoidal function and the lack of consideration for other factors that may affect the population.

Q14: How can the caribou population model be used in practice?

A14: The caribou population model can be used in practice to make predictions about future trends and understand the factors that affect the population. It can also be used to inform conservation efforts and management decisions.

Q15: What are some of the potential applications of the caribou population model?

A15: Some of the potential applications of the caribou population model include:

• Predicting future trends in caribou population
• Understanding the factors that affect the population
• Informing conservation efforts and management decisions
• Developing strategies for managing caribou populations

Conclusion

In this article, we have provided answers to frequently asked questions about the caribou population model. We hope that this information has been helpful in understanding the model and its applications. If you have any further questions, please don't hesitate to contact us.

References

• [1] Caribou Population Model. (n.d.). Retrieved from https://www.example.com
• [2] Sinusoidal Functions. (n.d.). Retrieved from https://www.example.com
• [3] Conservation Efforts. (n.d.). Retrieved from https://www.example.com

Glossary

• Caribou population model: A mathematical representation of the oscillating nature of the caribou population over time.
• Sinusoidal function: A mathematical function that represents a sinusoidal curve.
• Conservation efforts: Efforts to protect and preserve the caribou population and its habitat.