Why are we using exp(.) as the functional form in the household maximization problem inside the RCK model? Currently I'm studying the RCK model at my Advanced Macroeconomics I classes. 
A question arose almost immediately when I saw the utility function of a household in this model. 



The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so. 
Thank you really much in advance for your kind responses.
I guess you already know that $\exp(-\rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor

$$\exp(-\rho t)=\lim_{m \to \infty} \left(1+ \frac{\rho}{m}\right)^{mt}$$