How could i write a function to represent the increase by a certain percentage? e.g. given an amount x, and given an increase percentage (10% ), i want as a result [x + (x*10/100)] then at the next step is the new value + 10% of the new value and so on..
does this need differential equation?
How can I plot this?
Note in your example of $x + x\frac{10\%}{100\%}$ that it can be simplified to $x(1 + 0.1) = (1.1)x$. That is, instead of "adding 10% to $x$", this can be thought of as "multiplying $x$ by $1.1$".
More generally, if you want to increase by $p\%$, then you calculate $$r = 1 + \frac{p\%}{100\%} = 1+(0.01)p$$ And the increase operation is $x \mapsto rx$.
Now you talk about doing this in steps. So you have some starting value $x_0$, then you calculate the next values $$\begin{align}x_1 &= rx_0\\x_2 &= rx_1 = r(rx_0) = r^2x_0\\x_3 &= rx_2 = r(r^2x_0) = r^3x_0\\&\ \ \vdots\\x_n &= r^nx_0\end{align}$$
And that is your formula. The result of the $n$-th increase is $r^n x_0$.