Linear growth:

semantic: rate of change is constant.

graphic:

constant to rate of change

algorithmic: Rate:=const

Typical: The rate of change is constant.

Exponential growth:

semantic: rate of change is proportional to state variable.

graphic:

line from state variable to rate of change (feedback)

algorithmic: Rate:=Factor*State

Typical: feedback from the state variable to the rate of change.