Question

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.

Answer 1

While linear equations are always straight, nonlinear equations often feature curves.

Answer 2

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

`s=(d)/(t)`

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

`3=(d)/(t)\\ d=3t`

Where
`t` represents the independent variable (horizontal axis) because it represents time, and
`d` 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

`N(t)=N_(0) e^(rt)`

Where
`t` is time (horizontal axis),
`r` is growth rate,
`N_(0)` is the initial population and
`N(t)` is the population after
`t` time.

A specific example is

`N(t)=12e^(0.012t)`

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