The noise level, N, in decibels, of a rock concert is given by , where d is the distance in meters from the concert speakers. Which of the following gives the rate of change, in decibels per meter, of noise 600 meters away from the speakers?
C)d such that
D)d such that

Question

The noise level, N, in decibels, of a rock concert is given by  , where d is the distance in meters from the concert speakers. Which of the following gives the rate of change, in decibels per meter, of noise 600 meters away from the speakers?
C)d such that 
D)d such that

Quizplus · Accepted Answer

To find the rate of change of noise with respect to distance, we need to take the derivative of N with respect to d:

,

Using the power rule of differentiation, we get:

So the rate of change of noise with respect to distance is given by .

To find the value of this expression when d = 600, we substitute d = 600 into the derivative:

.

Simplifying this expression gives:

.

Therefore, the rate of change of noise 600 meters away from the speakers is given by .

Out of the answer choices, only (B) matches this expression, so the answer is (B).

The Noise Level, N, in Decibels, of a Rock Concert