Question

During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the population quadruples in 30.8 minutes, in how many minutes will the population quintuple?

Answer 1

The population will quintuple in 30.8 minutes.

Step-by-step explanation:

In exponential growth, the rate at which the population increases is proportional to the current population.

The time it takes for a population to double is called the doubling time.

In this case, the population quadruples in 30.8 minutes. So the doubling time is 30.8/2 = 15.4 minutes.

To find out how long it will take for the population to quintuple, we need to find the time for two more doublings.

Since the doubling time is 15.4 minutes, it will take 2*15.4 = 30.8 minutes for the population to double twice more.

So, the population will quintuple in 30.8 minutes.

Answer 2

The exponential function is given by P(t) = P0 e^kt; where P(t) is the current population, P0 is the initial population and t is the time.
Thus, P(t) / P0 = e^kt
4 = e^30.8k
ln 4 = 30.8k
k = ln 4 / 30.8 = 0.045

For the population to quituple,
5 = e^0.045t
ln 5 = 0.045t
t = ln 5 / 0.045 = 35.76

Therefore, it will take the population 35.76 minutes to quintuple.