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.
Situation 1:
A company manufactures bicycles. They produce a total of 100 bicycles each month. As the demand for bicycles increases, they decide to increase their production by 20 bicycles every month.
Situation 2:
A person is saving money in a bank account. Initially, they deposit $1000 and plan to save an additional 5% of the total amount in the account each month.
In Situation 1, the pattern is linear because the company increases their production by a fixed amount (20 bicycles) every month.
In Situation 2, the pattern is nonlinear because the person's savings increase by a percentage (5% of the total amount) each month, which will result in varying amounts saved depending on the total amount in the account.
Now, I will write a function that models the linear situation (Situation 1).
Let's assume the number of months is represented by 'x' and the total number of bicycles produced is represented by 'y'.
The function can be represented as:
y = 20x + 100
This function models the linear pattern in which the total number of bicycles produced (y) increases by 20 each month (the coefficient of 'x') and starts with an initial production of 100 bicycles (the constant term).
Now, I will provide an ordered pair that is a solution for this function:
Let's choose x = 3 (representing 3 months)
Substituting the value of x into the function:
y = 20(3) + 100
y = 60 + 100
y = 160
The ordered pair (3, 160) represents that after 3 months, the company will have produced a total of 160 bicycles.