What is the meaning of proportional and how is it used in different contexts?

[Instinctlol]

I hear teachers say something is proportional to something else. What does "proportional " mean? Can someone explain to me with some examples? Thanks !

 

[QuarkCharmer]

Proportional means that something changes with respect to something else. For instance, ants eat food, and the more food they eat the more they can reproduce. Thus, the population growth of the ants is proportional to the amount of food. You could also say that the population growth is "inversely proportional" to the amount of ant killer in their environment.

This is usually facilitated by use of a constant of proportionality, sometimes called k. When something is proportional to something else, it does not mean the values are equal, just that they change with respect to each other. The constant of proportionality serves as a multiplier.

If T is the population growth of ants, and P is the amount of food in their environment. You could say that:

$T∝P$

More specifically, that means that the values likely only differ by a constant, so you can say:

$T=kP$

An example of inversely proportional would be something like:
$T = k\frac{1}{M}$ where M is ant killer, poison, or whatever I said before.

Edited: Mistake corrected.

 

[Instinctlol]

Proportional means that something changes with respect to something else. For instance, ants eat food, and the more food they eat the more they can reproduce. Thus, the population growth of the ants is proportional to the amount of food. You could also say that the population growth is "inversely proportional" to the amount of ant killer in their environment.

This is usually facilitated by use of a constant of proportionality, sometimes called k. When something is proportional to something else, it does not mean the values are equal, just that they change with respect to each other. The constant of proportionality serves as a multiplier.

If T population growth of ants, and P is the amount of poison in their environment. You could say that:

$T∝P$

More specifically, that means that the values likely only differ by a constant, so you can say:

$T=kP$

An example of inversely proportional would be something like:
$T = k\frac{1}{M}$ where M is ant killer, poison, or whatever I said before.

Great explanation, thank you!

 

[QuarkCharmer]

I just realized that I made an error. This line:
"If T population growth of ants, and P is the amount of poison in their environment. You could say that:"

..should read "food" instead of poison! I hope you caught that one. I will edit my original post to be accurate.

 

[vela]

Note that proportional means the two variables are related by a constant factor. If Y is proportional to X, that always means Y=kX for some constant k.

A common misuse of the term by students is to take proportional to mean depends on. For example, if Y=X², they would say Y is proportional to X, which is not correct. If X varies, Y does too, but Y doesn't vary in the right way to say it's proportional to X.

 

[Borg]

I just realized that I made an error. This line:
"If T population growth of ants, and P is the amount of poison in their environment. You could say that:"

..should read "food" instead of poison! I hope you caught that one. I will edit my original post to be accurate.

Schrodinger slip?

 

[t.francis]

^ freudian slip. Stop mixing up your physicists and psychologists... unless your comment was in irony and I missed it? =P

As for an easy way to think about proportionality: as x increases, so does y AT A CONSTANT RATE

So time taken for a falling object to hit the floor is proportional to the square root of the height at which it was released.

Force is proportional to the product of mass and velocity.

To make a proportion sign into an equals sign you need to introduce 'k' as a constant.

 

[Borg]

^ freudian slip. Stop mixing up your physicists and psychologists... unless your comment was in irony and I missed it? =P

Yes, you missed it.