The graph of W = t2 + t + 1 is a simple parabola:

decibels graph

The graph of the sound pressure P,

`P=10\ log\ (t^2+t+1)/(10^(-12)`

is given by:

decibels graph

The derivative of P is given by:

`(dP)/(dt)=10[1/W log_10e](dW)/(dt)`

`=10[1/(t^2+t+1) log_10e]xx` `(d(t^2+t+1))/(dt)`

`=4.343(2t+1)/(t^2+t+1)`

At t = 3, the rate of change of P with respect to time is:

`(dP)/(dt)=[4.343(2t+1)/(t^2+t+1)]_(t=3)`

`=2.339\ "dB"//"s"`

The units are dB/s since the sound pressure is changing as time goes on.

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