Let G be a group acting properly on a metric space X and consider a path system of X. Assume that G contains a constricting element with respect to the path system. This talk will be about the relative exponential growth rates and the quotient exponential growth rates of the quasi-convex subgroups of G with respect to the path system. Through the triangle inequality, we will see that we can determine that the first kind of growth rates are strictly smaller than the growth rate of G, while the second kind of growth rates coincide with the growth rate of G. Examples of applications include relatively hyperbolic groups, CAT(0) groups and hierarchically hyperbolic groups containing a Morse element. This generalises work of Dahmani-Futer-Wise and Gitik-Rips.