A culture started with 6000 bacteria after 2 hours it grew to 7800 bacteria predict how many bacteria will be present after 15 hours

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.