Introduction to Functions Discussion
Before engaging in the discussion, view the Discussion Guidelines and the Discussion Rubric to ensure that you understand the expectations for this activity. Once you have posted your response, you are also required to respond to at least two other students’ posts. You may want to check back later to respond to your classmates.
1. Describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern. Do not state which situation is linear and which is nonlinear. Your classmates will need to determine which is which and then write a function that models the linear situation. Your classmates will also need to write 1 ordered pair that is a solution to the linear function and explain its meaning in the context of the situation.
For your original discussion post, you only need to respond to #1.
2. View posts from your classmates and choose one to respond to. You will need to determine which situation is linear and which situation is nonlinear. For the linear situation you will need to write a function that models it and then write 1 ordered pair that is a solution and explain its meaning in the context of the situation.
3. View responses and comment on the work of another classmate. You may correct any errors that you find, show another way to solve the problem, or provide constructive feedback on the work.
1. A situation that models a linear pattern could be the number of hours worked and the amount of money earned. As the number of hours worked increases, the amount of money earned also increases at a constant rate.
A situation that models a nonlinear pattern could be the growth of a population over time. Initially, the population may grow slowly, but as time goes on, the growth rate increases, resulting in exponential growth.
2. Response to classmate: From the descriptions given, I believe that the first situation (number of hours worked and amount of money earned) is the linear pattern, while the second situation (population growth over time) is the nonlinear pattern.
For the linear situation, let's assume that the function is represented by y = mx + b, where y is the amount of money earned, x is the number of hours worked, m is the hourly wage, and b is the base amount of money earned (such as a fixed salary).
Let's say the function is y = 15x + 100, where 15 is the hourly wage and 100 is the base amount of money earned. As an ordered pair solution, we can take (5, 175), where 5 represents 5 hours worked and 175 represents the amount of money earned. In this context, it means that if someone works for 5 hours, they would earn $175, considering the given hourly wage and base amount of money earned.
3. Response to another classmate: I reviewed your post and I agree with your determination of the linear and nonlinear situations. Your explanation and the function you provided for the linear situation is correct. However, it seems that you forgot to provide an ordered pair solution and its meaning in the context of the situation. Can you please provide one so that we can have a complete understanding of the linear pattern?