Question

A scientist studied bacteria.She placed 4 bacteria in a dish.The population of bacteria triples every 12 hours.Which equation can be used to determine the number of bacteria, y, present after x days?

Answer 1

The general equation for an exponential growth is,

`P=P_0r^{(t)/(T)}`

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

`y=4(3)^(2x)`

Hence, option C is correct.