Select The Correct Answer.A Particular Strain Of A Common Bacteria Replicates Itself Every 14 Minutes. Which Of The Following Describes This Situation?A. Neither A Relation Nor A FunctionB. A Relation OnlyC. A Function OnlyD. Both A Relation And A Function
In the realm of biology, particularly in the study of microorganisms, understanding the concepts of relations and functions is crucial. A relation is a set of ordered pairs that describe the relationship between two variables, while a function is a specific type of relation where each input corresponds to exactly one output. In this article, we will delve into the concept of a particular strain of a common bacteria that replicates itself every 14 minutes and determine whether this situation describes a relation, a function, or both.
What is a Relation?
A relation is a set of ordered pairs that describe the relationship between two variables. In the context of biology, a relation can be used to describe the relationship between a variable, such as the time it takes for a bacteria to replicate, and another variable, such as the number of bacteria present. For example, if we have a relation R = {(0, 1), (14, 2), (28, 4), ...}, where the first element of each ordered pair represents the time in minutes and the second element represents the number of bacteria present, we can say that this relation describes the relationship between the time it takes for the bacteria to replicate and the number of bacteria present.
What is a Function?
A function is a specific type of relation where each input corresponds to exactly one output. In other words, for every input, there is only one possible output. In the context of biology, a function can be used to describe the relationship between a variable, such as the time it takes for a bacteria to replicate, and another variable, such as the number of bacteria present. For example, if we have a function f(t) = 2^t/14, where t represents the time in minutes and f(t) represents the number of bacteria present, we can say that this function describes the relationship between the time it takes for the bacteria to replicate and the number of bacteria present.
The Situation: A Particular Strain of a Common Bacteria
A particular strain of a common bacteria replicates itself every 14 minutes. This means that if we start with a single bacteria, after 14 minutes, we will have two bacteria, after 28 minutes, we will have four bacteria, and so on. This situation can be described using a relation or a function.
Is This Situation a Relation or a Function?
To determine whether this situation is a relation or a function, we need to examine the relationship between the time it takes for the bacteria to replicate and the number of bacteria present. In this case, we can see that for every input, there is only one possible output. For example, if we input 14 minutes, the output is 2 bacteria, if we input 28 minutes, the output is 4 bacteria, and so on. This means that this situation can be described using a function.
Why is This Situation a Function?
This situation is a function because each input corresponds to exactly one output. In other words, for every input, there is only one possible output. This is in line with the definition of a function, which states that a function is a specific type of relation where each input corresponds to exactly one output.
Why is This Situation Not a Relation?
This situation is not a relation because a relation is a set of ordered pairs that describe the relationship between two variables, but it does not guarantee that each input corresponds to exactly one output. In other words, a relation can have multiple outputs for a single input, which is not the case in this situation.
Conclusion
In conclusion, a particular strain of a common bacteria that replicates itself every 14 minutes can be described using a function. This is because each input corresponds to exactly one output, which is in line with the definition of a function. Therefore, the correct answer is C. A function only.
Key Takeaways
- A relation is a set of ordered pairs that describe the relationship between two variables.
- A function is a specific type of relation where each input corresponds to exactly one output.
- A particular strain of a common bacteria that replicates itself every 14 minutes can be described using a function.
- Each input corresponds to exactly one output in this situation, which is in line with the definition of a function.
Further Reading
For further reading on relations and functions in biology, we recommend the following resources:
- [1] "Relations and Functions in Biology" by [Author's Name]
- [2] "Biology: The Dynamics of Life" by [Author's Name]
- [3] "Mathematics for Biology" by [Author's Name]
References
[1] "Relations and Functions in Biology" by [Author's Name] [2] "Biology: The Dynamics of Life" by [Author's Name] [3] "Mathematics for Biology" by [Author's Name]
Appendix
A. Neither a relation nor a function B. A relation only C. A function only D. Both a relation and a function
In our previous article, we explored the concept of relations and functions in biology, particularly in the context of a particular strain of a common bacteria that replicates itself every 14 minutes. We determined that this situation can be described using a function, as each input corresponds to exactly one output. In this article, we will answer some frequently asked questions (FAQs) related to relations and functions in biology.
Q: What is the difference between a relation and a function?
A: A relation is a set of ordered pairs that describe the relationship between two variables, while a function is a specific type of relation where each input corresponds to exactly one output.
Q: Can a relation have multiple outputs for a single input?
A: Yes, a relation can have multiple outputs for a single input, which is not the case in a function.
Q: How do I determine whether a situation is a relation or a function?
A: To determine whether a situation is a relation or a function, you need to examine the relationship between the input and output variables. If each input corresponds to exactly one output, then it is a function. If there are multiple outputs for a single input, then it is a relation.
Q: Can a function have multiple inputs?
A: Yes, a function can have multiple inputs, but each input must correspond to exactly one output.
Q: Can a relation have multiple inputs?
A: Yes, a relation can have multiple inputs, but it does not guarantee that each input corresponds to exactly one output.
Q: What is an example of a relation in biology?
A: An example of a relation in biology is the relationship between the amount of sunlight a plant receives and its growth rate. This relationship can be described using a set of ordered pairs, but it does not guarantee that each input corresponds to exactly one output.
Q: What is an example of a function in biology?
A: An example of a function in biology is the relationship between the time it takes for a bacteria to replicate and the number of bacteria present. This relationship can be described using a function, as each input corresponds to exactly one output.
Q: Can a function be used to model a real-world phenomenon?
A: Yes, a function can be used to model a real-world phenomenon. For example, a function can be used to model the growth of a population over time, the spread of a disease, or the behavior of a physical system.
Q: What are some common applications of functions in biology?
A: Some common applications of functions in biology include:
- Modeling population growth and decline
- Studying the spread of diseases
- Analyzing the behavior of physical systems, such as the movement of molecules
- Understanding the relationships between variables in a biological system
Q: How can I learn more about relations and functions in biology?
A: There are many resources available to learn more about relations and functions in biology, including textbooks, online courses, and research articles. You can also consult with a biology professor or a mathematician for guidance.
Conclusion
In conclusion, relations and functions are fundamental concepts in biology that can be used to describe and analyze complex biological systems. By understanding the difference between a relation and a function, you can better appreciate the beauty and complexity of biological systems. We hope this Q&A article has been helpful in answering your questions and providing a deeper understanding of relations and functions in biology.
Key Takeaways
- A relation is a set of ordered pairs that describe the relationship between two variables.
- A function is a specific type of relation where each input corresponds to exactly one output.
- Relations and functions can be used to model real-world phenomena in biology.
- Functions can be used to analyze and understand complex biological systems.
Further Reading
For further reading on relations and functions in biology, we recommend the following resources:
- [1] "Relations and Functions in Biology" by [Author's Name]
- [2] "Biology: The Dynamics of Life" by [Author's Name]
- [3] "Mathematics for Biology" by [Author's Name]
References
[1] "Relations and Functions in Biology" by [Author's Name] [2] "Biology: The Dynamics of Life" by [Author's Name] [3] "Mathematics for Biology" by [Author's Name]
Appendix
A. What is the difference between a relation and a function? B. Can a relation have multiple outputs for a single input? C. How do I determine whether a situation is a relation or a function? D. Can a function have multiple inputs?
The correct answers are:
A. A relation is a set of ordered pairs that describe the relationship between two variables, while a function is a specific type of relation where each input corresponds to exactly one output. B. Yes, a relation can have multiple outputs for a single input. C. To determine whether a situation is a relation or a function, you need to examine the relationship between the input and output variables. D. Yes, a function can have multiple inputs.