The decibel rating $D$ is related to the sound intensity $I$ by the formula $\displaystyle D = 10 \log_{10} \left( \frac{ I }{ 10^{-16} } \right)$ for the noise level in decibels.

(a) Let $D$ and $d$ represent the decibel ratings of sounds of intensity $I$ and $i$, respectively. Using properties of logarithms, find a simplified formula for the difference between the two ratings, $D - d$, in terms of the two intensities $I$ and $i$.
$D - d =$ help (logarithms) (Enter log10 or logten for the base 10 logarithm.)

(b) If a sound's intensity doubles, how many decibels louder does the sound become?
decibels help (numbers)