The temperature of an object cooling in a room is modeled by $T(t)=R+(I-R)k^t$, where $T(t)$ is the temperature at time $t$, $R$ is the room temperature, $I$ is the initial temperature of the object, and $k$ is a constant ($0<k<1$). If the initial temperature of the object is increased, but the room temperature and the constant $k$ remain the same, which of the following statements must be true?