What may be this line's equation?

Question

I have a line like this:

The values are not perfect (means the values can be changed), but all are non-negative values. I like to know the equation's equation or function.

I have tried-

$y=\ln(x)$

$y=e^x$

$y=\sin(x)$

$y=\tan(x)$

But nothing is matching this equation so much. I am thinking it may be some kind of transformations of $y=1/e^x$, but I am not sure about it.

So, can anyone please help me to find the equation formula, please?

Thanks in advance for helping :)

Answer 1

I have solved it like this-

$$f(x) = ab^{x}$$

Where: $$ a > 0 $$ $$ 0< b < 1 $$ $$ x\ge 0 , x \in Z $$

More can be found in here.

Answer 2

Try $$f(x) = \begin{cases}\frac1{x^k} & x > 0 \\ 0 & x\le0 \end{cases}$$

where $k > 0$ or

$$f(x) = \begin{cases}e^{-kx} & x \ge 0 \\ 0 & x <0 \end{cases}$$

Answer 3

Using the form $$y=\frac1{x+c}-\frac1{x_0+c},$$ we find $$c=\frac12\left(\sqrt{x_0^2+\frac{4x_0}{y_0}}-x_0\right),$$ where $x_0$ and $y_0$ are the $x$ and $y$ intercepts respectively.

You can view this equation modelling your line here.