In the laser simulation when pumping photons into a two-state system, you could adjust the lifetime of how long an excited atom stays excited before it releases its energy in the form of a photon. if you decrease the lifetime of the excited state, what happens?

there won't be enough atoms that are excited around to undergo stimulated emmision

Explanation:

Stimulated Emission is the process used in laser operations to produce photons.

In stimulated emission a passer-by photon stimulates the atom to emit a photon, identical to the passer-by photon, immediately. The con to this is that the same passer-by photon could instead get absorbed by a de-excited atom.  Therefore, aside of atom excitation we need to use witty ways to insure that there are more excited atoms that could use the passer-by photon for stimulated emission than there are de-excited atoms.

Photons produced by this stimulation have the same wavelength which enables efficiency as all photons are emitted into the same node.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .