Function Type

[kolopoi0]

Good night,

I would like to know what function type is e^-ax-bx2

I was thinking that this is an exponential function, but sometimes it is called "Linear Quadratic"? - Usually this happens when it is plotted in a log - linear plot.

Thank you very much for your help.

 

[Steven G]

I think that a 'Linear Quadratic' is a system of two equations where one equation is linear and one is quadratic.
I know that e^x is called an exponential equation so I guess that e^-ax-bx2is exponential

 

[kolopoi0]

I think that a 'Linear Quadratic' is a system of two equations where one equation is linear and one is quadratic.
I know that e^x is called an exponential equation so I guess that e^-ax-bx2is exponential

I also thought this, but there are some "rules" that need to be satisfied before we can call it "exponential" right? By any chance do you know if this specific function satisfies them? I am just guessing

 

[topsquark]

I also thought this, but there are some "rules" that need to be satisfied before we can call it "exponential" right? By any chance do you know if this specific function satisfies them? I am just guessing

An expression is called "exponential" if we have e raised to some power, such as [math]e^{x}[/math], [math]e^{-x}[/math], [math]e^{-x^2/(2d)}[/math], etc. More loosely you can get away with calling [math]a^x[/math] an exponential function, where [math]a \neq e[/math] is a constant. As a Physicist I only ever see the word "exponential" when the base is e.

-Dan

 

[Dr.Peterson]

I also thought this, but there are some "rules" that need to be satisfied before we can call it "exponential" right? By any chance do you know if this specific function satisfies them? I am just guessing

Why does it matter what the name is? Will it affect something you plan to do?

Most things don't have specific names; names of function types are often not well defined, or are too narrow to include everything you can imagine. This function is a composition of an exponential function (which I would consider any [MATH]a^x[/MATH]) and a polynomial. It is not a pure exponential as I think of it, but depending on the reason you need a name, that may or may not matter.

So, what will you do once you are sure of the name, that you can't do without it? (That's not just a rhetorical question.)

 

[kolopoi0]

Why does it matter what the name is? Will it affect something you plan to do?

Most things don't have specific names; names of function types are often not well defined, or are too narrow to include everything you can imagine. This function is a composition of an exponential function (which I would consider any [MATH]a^x[/MATH]) and a polynomial. It is not a pure exponential as I think of it, but depending on the reason you need a name, that may or may not matter.

So, what will you do once you are sure of the name, that you can't do without it? (That's not just a rhetorical question.)

This equation is actually used to model cell survival after an exposure to ionizing radiation. We were discussing in class which type of function it was, an even though in radiobiology we call it a "Linear - Quadratic", I was convinced it was an exponential. So that is why I was actually wondering what kind of function it was, and was looking into some math definitions to better understand the concept.

Note: We call it "Linear - Quadratic" because it is usually plot in a log - linear scale

 

[Dr.Peterson]

I tried searching to see where these terms are used, in order to understand your context better. The first place I found, clearly related to your own context, is in https://www.sciencedirect.com/topics/medicine-and-dentistry/loglinear-model (in the article "Radiobiology of Lung Cancer").

It appears that "linear-quadratic" here is not meant as a general "type of function", but as an ad-hoc name for this particular model based on its log having a linear term and a quadratic term. That is, it is not "a linear-quadratic function" (suggesting that it is an example of a general category about which more is known), but "the linear-quadratic model" that has been developed for this particular phenomenon based on experimental data.

Note that this paper actually calls it "the following exponential function"!

 

[kolopoi0]

I tried searching to see where these terms are used, in order to understand your context better. The first place I found, clearly related to your own context, is in https://www.sciencedirect.com/topics/medicine-and-dentistry/loglinear-model (in the article "Radiobiology of Lung Cancer").

It appears that "linear-quadratic" here is not meant as a general "type of function", but as an ad-hoc name for this particular model based on its log having a linear term and a quadratic term. That is, it is not "a linear-quadratic function" (suggesting that it is an example of a general category about which more is known), but "the linear-quadratic model" that has been developed for this particular phenomenon based on experimental data.

Note that this paper actually calls it "the following exponential function"!

Thank you very much! Solved