The noise level in a library is $40$ decibels (dB), while the noise level in a busy restaurant is $70$ decibels (dB). The formula for sound intensity level in decibels is $\beta = 10 \log_{10}\left(\frac{I}{I_0}\right)$, where $I$ is the sound intensity and $I_0$ is the reference intensity. How many times more intense is the sound in the restaurant compared to the library?