Try functions like pchip or spline. This does a piecewise polynomial approximation that goes through all the data. If you want instead a smooth function that approximates your data by combining two sub-functions, I would try a function of the following form
f(x) = f1(x)*(sfn(x-xh)) + f2(x)*(1-sfn(x-xh))
Here, f1 is your exponential, f2 is the polynomial approx., and sfn is the as yet undetermined smoothing function which will smoothly vary from 1 to 0 at the specified xh.
The trick now is to find a suitable smoothing fn that transition from 0 to 1 or vice versa. 1-exp(-x/tau) is a smooth transition from 0 to 1, but only for x>0 -- you can limit this using a max() function. Tau sets the rate of transition. You can also try a simple ramp-in function: sfh=k*(x-xh)-- once again you have to bound it between 0 and 1: sfh=max(min(k*(x-xh),1),0). If you want to get fancy, try a second order equation with initial and final slope=0.
