Goal

Create an exposure tool which affects values above a specified threshold point $(t0, t0)$.
Values below the threshold point will remain unaffected.
Values above some upper the threshold point $(x1, y1)$ will be linear, with a slope defined by the exposure.
Values between $t0$ and $x1$ will be smoothly joined by a quadratic function.

Result

https://www.desmos.com/calculator/65gtfb7wxy

Solve

Power Function

We start with a simple power function, also known as a quadratic function: f$\left(x\right)=ax^{p}+b$ : https://www.desmos.com/calculator/4bxs46dtjp

https://www.desmos.com/calculator/zjcfqksu8w

$a$ controls the slope. $b$ controls the vertical y offset. $p$ controls the curve between $b$ and $(1, a)$.

We will use this function to join our linear section below our threshold point, and our linear section where slope = exposure, above our falloff point.

Derivative

The first thing we need to do is figure out the coordinate on our curve where the slope equals some value. We need this information to accurately position our splice point so that the slopes between the linear section and the quadratic match.

To do this we will use the derivative of this function. The derivative describes the slope of a function at some coordinate. To find the derivative (since I have only basic math skills) we will use the help of wolframalpha: derivative(y=a*x^p+b)