What model describes the relationship between the amount of bacteria and time, given that the bacteria quadruple every two hours? linear quadratic cubic exponential

For this case we have a function of the form:
 y = A * (b) ^ t
 Where,
 A: initial amount of bacteria
 b: growth rate
 t: time
 Rewriting the equation for this case we have:
 y = A * (4) ^ ((1/2) t)
 
 A model that describes the relationship between the amount of bacteria and time is:
 exponential