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.
Situation 1: A company manufactures and sells t-shirts. They sell the t-shirts for $10 each. The number of t-shirts sold each month is recorded for a year.
Situation 2: A car is accelerating from 0 to 60 mph. The car's speed is measured at different time intervals during the acceleration process.
In Situation 1, the number of t-shirts sold per month is likely to have a linear pattern as the price per t-shirt remains constant. In Situation 2, the car's speed will not have a constant rate of change, so it is likely to have a nonlinear pattern.
To model the linear situation, we can write a linear function: f(x) = 10x, where x represents the number of months and f(x) represents the number of t-shirts sold.
As an example, let's say that after 3 months, the company sold 300 t-shirts. This means f(3) = 300. In the context of the situation, this means that after 3 months, the company sold 300 t-shirts.
pick a different one
Situation 1: A flower shop sells bouquets of roses. The price of each bouquet is $20. The number of bouquets sold each day is recorded for a month.
Situation 2: A person goes on a road trip and records the distance traveled at different time intervals along the journey.
In Situation 1, the number of bouquets sold per day is likely to have a linear pattern as the price per bouquet remains constant. In Situation 2, the distance traveled will not have a constant rate of change, so it is likely to have a nonlinear pattern.
To model the linear situation, we can write a linear function: f(x) = 20x, where x represents the number of days and f(x) represents the number of bouquets sold.
As an example, let's say that on the 5th day, the flower shop sold 100 bouquets. This means f(5) = 100. In the context of the situation, this means that on the 5th day, the flower shop sold 100 bouquets.
Which is linear/nonlinear
Situation 1: A car is accelerating from 0 to 60 mph. The car's speed is measured at different time intervals during the acceleration process.
Situation 2: A person saves money each month. The amount of money saved is recorded for a year.
Situation 1 is nonlinear, as the speed of the car is changing at different rates over time during the acceleration process. Situation 2 is linear, as the amount of money saved each month is likely to have a constant rate of change, assuming the person saves the same amount each month.
Sure! Let's start with a situation that models a linear pattern:
Suppose you are calculating the total cost of items at a grocery store. Each item costs $2, and you want to find the total cost based on the number of items purchased. The number of items is the independent variable, and the total cost is the dependent variable. As the number of items increases by one, the total cost increases by $2.
Now, let's move on to a situation that models a nonlinear pattern:
Imagine you are tracking the growth of a plant over time. Initially, the plant grows slowly, but as time goes on, its growth rate accelerates. The time is the independent variable, and the plant's height is the dependent variable. As time increases, the plant's height does not increase at a constant rate but instead increases at an increasing rate.
In this task, you need to determine which situation exhibits a linear pattern and write a function to model it. Once you have identified the linear situation, you can write the linear function using the given information.