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

Answer:

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

$s=\frac{d}{t}$

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

$3=\frac{d}{t}\\ d=3t$

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.

Answer 2

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