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.
1. Situation A: Suppose you are driving a car and its speedometer is constantly increasing by 10 mph every hour. This situation models a linear pattern because the increase in speed is consistent and can be represented by a straight line on a graph.
Situation B: Imagine you are filling a bathtub with water. At first, the water fills up slowly, then the rate of filling increases rapidly, and finally, it slows down again as the bathtub approaches being full. This situation models a nonlinear pattern because the rate of filling is not constant and cannot be represented by a straight line on a graph.
2. In response to another classmate's post, let's assume that Situation A (the car's increasing speed) is the linear pattern and Situation B (the filling bathtub) is the nonlinear pattern.
For Situation A (linear pattern with the car's increasing speed), we can write a function to model this situation:
f(t) = 10t, where f(t) represents the speed of the car (in mph) at time t (in hours).
Let's choose the ordered pair (2, 20) as a solution to this linear function. In the context of the situation, it means that after 2 hours of driving, the car's speed will be 20 mph.