# 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.

• It's just there for bringing future utility to present value in continuous time. $\rho$ is the discount factor. – Pedro Cavalcante Dec 2 '18 at 22:47

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