I want an exponential function which passes through (0,p) and (n-1,1-p), where p is a constant in range [0,1]. The following function met this requirement:
$$y = p\left(\frac{1-p}{p}\right)^{\frac{x}{n-1}}$$
But I want to include another variable s in [0,1] in this function which controls the slope (derivative) of the function. How can I change the function to include this variable?