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.

When we talk about linear patterns, we refer to those events where events are related with a linear proportion, that is, if one magnitude increases, the other one will to, or if one magnitude increases the other would decrease, and this behaviour with a linear function which is represented as a line.

So, one example of linear model would be speed, which relates distances and time in a linear behaviour, which function is

So, if one ball has a speed of 3 meters per second, the function would be

Where represents the independent variable (horizontal axis) because it represents time, and is distance, which is a dependent variable.

On the other hand, a non linear model could be population growth, which is an exponential beahaviour. It's not represented with a linear function, that's why is not linear.

An example of a function that represents population growth is

Where is time (horizontal axis), is growth rate, is the initial population and is the population after time.

A specific example is

At last, each function graph is attached, there you could see a lot better, the linear and non-linear behaviour.