Bot . 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.
Situation 1 (Modeling a Linear Pattern):
In a grocery store, a customer is shopping for apples. The customer notices that as they increase the number of apples they buy, the cost of the apples also increases linearly. For example, if the customer purchases 2 apples, the cost is $2. If they purchase 4 apples, the cost is $4. Similarly, if they buy 6 apples, the cost is $6. This pattern continues.
Situation 2 (Modeling a Nonlinear Pattern):
A child is riding a Ferris wheel at an amusement park. The child notices that as the ride progresses, the height they are at changes in a nonlinear pattern. The height increases rapidly at the beginning, reaching the highest point, then gradually decreases as the ride comes to an end. The change in height is not constant and varies with time.
Situation 1: In this situation, a car rental company charges customers a fixed daily rate for renting a car. The total cost is directly proportional to the number of days the car is rented.
Situation 2: In this situation, a manufacturer produces toys and sells them to a distributor. The manufacturer offers a bulk discount to the distributor, where the more toys the distributor buys, the lower the cost per toy.
Please note that the linear pattern corresponds to Situation 1, while the nonlinear pattern corresponds to Situation 2. It is up to your classmates to determine which is which and proceed with writing the linear function and identifying an ordered pair solution.
Sure! Here are two different situations, one that models a linear pattern and another that models a nonlinear pattern. I won't explicitly state which situation is which, so your classmates can determine that on their own.
Situation 1:
You are walking in a park and decide to track the number of steps you take every minute. As you walk, you notice that the number of steps increases by the same amount every minute. You record the following data:
Time (minutes) | Number of Steps
---------------|---------------
0 | 100
1 | 130
2 | 160
3 | 190
Situation 2:
You are painting a mural on a wall, and you keep track of the time it takes to paint different sections of the mural. As you paint, you observe that the amount of time it takes for each section is not consistent. You record the following data:
Section Number | Time Taken (minutes)
---------------|--------------------
1 | 5
2 | 8
3 | 12
4 | 17
Now, it's up to your classmates to determine which situation represents the linear pattern and nonlinear pattern. Once they figure that out, they can proceed to write a function that models the linear situation and provide one ordered pair as a solution.
If Situation 1 is determined to be the linear pattern, a function that models this situation could be:
Let 'x' represent the time in minutes, and 'y' represent the number of steps taken.
The general form of a linear equation is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
By examining the data, we can find the slope:
m = (Change in y) / (Change in x) = (130-100) / (1-0) = 30
Now, we can substitute the slope value and any point from the data into the equation and solve for 'b'. Let's choose (0, 100) as an ordered pair:
100 = 30 * 0 + b
b = 100
So, the linear equation that models the situation is:
y = 30x + 100
For the chosen ordered pair (0, 100), it means that at the starting time (0 minutes), you have already taken 100 steps.
I hope this helps your classmates to determine and solve the linear pattern! If you have any more questions, feel free to ask.