20 mph speed limit.

[Ming the Merciless]

But at the same time, if anything is growing at an exponential rate, that just means any function with an exponent > 1.

Now you are confusing loose English with the mathematical definitions. In maths that is not the definition of exponential, though for a simple layman they may think that.

For instance by your sentence above, below would be exponential growth but it is not

 

[roubaixtuesday]

You might want to check the definition of "exponential".

Cambridge University dictionary seems to think that x cubed is an exponential function.

They're also wrong

 

[roubaixtuesday]

Yes it is.

Exponential just means that the rate of increase keeps increasing.

So even a square function is exponential, never mind a cube function.

No, it doesn't. This is absolutely wrong mathematically.

Many functions display an increasing rate of increase.

A simple square function does.

An exponential displays a constant doubling time.

Eg 1,2,4,8,16,32,64

A square function would be
1,4,9,16,25,36

These both have positive and increasing rates of increase.

Only the first is exponential.

These are basic mathematical definitions.

 

[roubaixtuesday]

Definition of exponential function from wiki.

Note that no polynomial, not square, not cubic etc meets this definition.

They are fundamentally different

https://en.m.wikipedia.org/wiki/Exponential_function

 

[roubaixtuesday]

An exponent is the number something is to the power of. Thus, "to the power of 3" ie "cubic" is exponential

Is wrong. See above wiki.

Cubic is polynomial:

https://en.m.wikipedia.org/wiki/Polynomial

 

[Ming the Merciless]

Definition of exponential function from wiki.

Note that no polynomial, not square, not cubic etc meets this definition.

They are fundamentally different

https://en.m.wikipedia.org/wiki/Exponential_function

Yay someone else who understands.

 

[Profpointy]

Yay someone else who understands.

Actually you are quite right!
I was muddled up

 

[Profpointy]

No cubic means the max power will be three but powers of 2 or linear may also apply. For instance y = x ^ 3 - 16x^2 + 235x - 42 is cubic and somewhat different to y = 12 ^ x

Was confused by the word "max" but I see what you mean now in the context of a polynomial equation.

Agree on "exponential growth" too; as you say different from simply having an exponent

 

[Ming the Merciless]

Actually you are quite right!
I was muddled up

My degree is maths and these sort of things I should post in the thread on things that irritate you… 😁

 

[Alex321]

Now you are confusing loose English with the mathematical definitions. In maths that is not the definition of exponential, though for a simple layman they may think that.

For instance by your sentence above, below would be exponential growth but it is not


View attachment 707108

The English usage is not always the same as the mathematical usage, and this is one case of that.

 

[Ming the Merciless]

The English usage is not always the same as the mathematical usage, and this is one case of that.

The incorrect use, as you demonstrated

 

[Profpointy]

My degree is maths and these sort of things I should post in the thread on things that irritate you… 😁

Sadly so is mine (but don't tell anyone)

 

[roubaixtuesday]

Is there any feedback from Welshielands about how this 20mph speed limit is going?
Has the country ground to a standstill?
Have billions been received into the Cymru coffers as a result of all these fines?
Are there riots on the streets?

Every other 20mph change of this type was popular before implementation and even more popular afterwards.

Regardless of whining by loudmouthed petrolheads

 

[Alex321]

The incorrect use, as you demonstrated

Only incorrect when talking in Mathematics.

Perfectly correct when talking in English.

Various dictionaries agree, but presumably you will claim they are also incorrect, and don't know the English definition of words.

Go to a technical or scientific dictionary, as opposed to a normal English one, and the mathematical definition will be there (as is the case in my copy of Chambers Dictionary of Science and Technology).

 

[Drago]

Speaking in mathematics, not talking.