For bacterial growth, the kinetics follows the first order reaction whose equation is:
ln C = lnC0 + kt, where C and C0 are the population of bacteria after and at the start of time, respectively. The reaction constant is denoted as k.
We substitute C0 = 6000, C = 7800 and t=2 hours to determine k.
ln 7800 = ln(6000) + k(2)
k = 0.1312
Since we already know k, we use this value to find C when t=15 hours
ln C = ln(6000) + 0.1312(15)
C = 42,938
Thus, after 15 hours, the population of bacteria becomes 42,938.