I'm a programmer working on a calculation with a curve trend. I'm using OpenOffice Calc (like MS Excel) and it's given me a formula for a graph that I don't understand. I can't find this form anywhere.
Here is the chart:
I don't recognize that formula. the exp() part is part of the program syntax I think.
The documentation for it says:
returns 2.71828182845904, the mathematical constant e to Calc's accuracy.
Can anyone tell me what this formula is called and how it works? It's been a long time since my math classes.
expis the exponential function, also sometimes known as the natural antilogarithm. Usually mathematicians write it as $e^x$ instead of $\exp(x)$, but it's the same thing.It has various possible definitions -- one of them is that $x\mapsto e^x$ is the function that is its own derivative and maps $0$ to $1$.
The particular numbers in your function are probably ones that the program has chosen for you such that the function approximates the data points you've asked it to fit to. Using power laws we can also write it as
$$ 0.5146699145 \cdot e^{2.0438257176 x} = 0.5146699145\cdot 7.72008765^x $$ because $e^{2.0438257176} \approx 7.72008765$.
In general this kind of function is known as an exponential growth function. The constant $0.514...$ is the value of $f(0)$; you can call it the $y$-intercept or "initial value" or something like that.
The factor $2.043...$ is called the growth constant. In some contexts it makes better sense to think of dividing by $0.489...$ than multiplying by $2.043...$; in that case $0.489...$ is the characteristic time of the exponential growth, and it is measured in the same units as your $x$ input.