If the sound level at a point is 115 dB, what is the intensity of sound at that point?
(Unit=W/m^2)

The intensity of the sound is .

Explanation:

The equation for the decibel scale is

where is the intensity of sound, and is the intensity of the least audible sound to the human ear.

Now, we are told that at a certain point the sound level is 115dB; therefore,

,

which we simplify and solve for as follows:

which is the intensity of the sound at the point in question.

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 .