The intensity of a lightbulb in lumens, l, at time t in minutes is given by l(t) = 4 cos t + 2700. Approximately how much is the intensity changing after 20 minutes?

The rate of change is the derivative of the intensity function: l′(t) = −4 sin t. At t = 20 minutes, l′(20) = −4 sin(20) ≈ −4(0.913) ≈ −3.7 lumens per minute. So the intensity is decreasing at approximately 3.7 lumens per minute.

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