The intensity of a sound is given by

Question

The intensity of a sound is given by

I(t) = 4.343ln(100 + 250t²)

where I is in decibels and t is in minutes. At what rate is the sound's intensity changing at the instant t = 10 minutes? Be accurate to three decimal places and include correct units.

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Answer 1

We need the rate of change of Intensity I with respect to time t.

So, we need to find dI / dt.

I(t) = 4.343 ln ( F(t) )

where F(t) = 100 + 250 t^2

So, recall that d / dt { ln t } = 1 / t for the simple variable t (not quite the function F(t)).

Recall that you will need to use the chain rule after taking the derivative of ln ( F(t) ).

Then you have dI(t) / dt. You can plug in t=10 mins.

The units are just decibels / min