Is y=2^x a growth or decay?

as #x# increases, #2^x# also increases.

the smallest value of #2^x# is found when #x# tends to #-oo#. when this happens, #2^x# tends to #0#.

the largest value of #2^x# is found when #x# tends to #oo#. when this happens, #2^x# also tends to #oo#.

this is the graph for #y = 2^x:#

graph{2^x [-10, 10, -5, 5]}

it is visible here that #y# increases as #x# increases. #y# grows as #x# grows.

this may be found in situations of time.

an example is the process of binary fission that bacteria use to reproduce. it takes a certain amount of time for a bacterium to undergo binary fission; after this, there are two bacteria present. this goes on to form #4# bacteria, and #8#, and so on.

if you were to draw a graph to model this, #y# would be the number of bacteria present after #x# number of divisions.

at the start, there will be #1# bacterium - this is when #0# divisions have taken place. #2^0 = 1#.

after #1# division, there will be #2# bacteria. #2^1# = 2#

the graph would start at #(0,1)# and form an upward curve from there, since there cannot be negative processes of binary fission that have taken place.

this is the same for time - modelling a time-number graph (e.g. population over a given time) would start at an #x#-coordinate of #0# (when no time had passed) and a #y#-coordinate that shows the starting population.