I want to be able to manipulate the point of inflection of an exponential curve equation:$$a\exp\{xb\}.$$ could somebody tell me which parameter I may introduce in such a formula in order to make the resultant curve more bent, without changing anything else?
This pic represents what I want to do with the curve
You can multiply your exponential with a second degree polynomial, $x^2$: $$f(x)=x^2ae^{bx+c}$$
You can then fiddle with $c$ to slide the whole graph left again. For example, open this Desmos-link in two different tabs and leave one of them as is. Then multiply the function in the other by $x^2$ and change $c$ to around $-5.7$. Now change between the two tabs to see the change.