The rate of change of a function is its derivative. Saying that "The rate of change R, in km/hr, of the altitude of a hot air balloon is given by " means that, taking h(t) to be the altitude (in km) at time t (in hours), . Take the "anti-derivative" to find h(t). Of course, that will involve a arbitrary "constant of integration". Use "Assume the balloon is initially at ground level" to find that constant.