Question

Is y=2^x a growth or decay?

Answer 1

growth

Explanation:

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.