apace /əˈpeɪs/ (adv):

# (formal) ​at a fast speed; quickly.

to continue/ grow/ proceed/ develop apace

The privatization of state companies continued apace.

rapidly /ˈræpɪdli/ (adv): 

# ​very quickly; at a great rate.

to increase/spread/expand rapidly

to change/develop/evolve rapidly

a rapidly growing economy

Crime figures are rising rapidly.

It rapidly became apparent that there were insufficient officers to maintain control.

The technology is rapidly changing.