The general equation for an exponential growth is,
[tex]P=P_0r^{\frac{t}{T}}[/tex]Here, P is the population after t time, r is the rate of growth t is the time period over which the population is studied and T is the time taken for the population to become r times and Po is the initial population.
Given, the initial poulation of bacteria, Po=4.
The rate of increase in bacteria, r=3 times.
Let t be in days. So, t=x.
There are 24 hours in a day.
It takes 12 hours to triple. So, the time T=1/2 days.
So, the number of bacteria y after x days is
[tex]y=4(3)^{2x}[/tex]Hence, option C is correct.
