The rate of growth of a specific bacteria population in a petri dish, $G(t)$ in thousands of bacteria per hour, is modeled by the function

$$G(t)=\frac{12}{2+\sqrt{2t+4}}$$

for $0\le t\le 16$, where $t$ is the time in hours since the start of the experiment. Using the substitution $u=2+\sqrt{2t+4}$, find the exact total increase in the population over the 16-hour period by calculating the value of

$${\int }_0^{16}\frac{12}{2+\sqrt{2t+4}}dt$$

Give your answer in the form $a+b\ln c$, where $a,b,$ and $c$ are integers.