Question

Hello, could someone please help me approach this problem? I'm not sure if there's a specific formula or methodology I should be using. Thank you!

An organism produces 4 progeny every time it reproduces, and its generation time is 30 minutes. If you start with 10 organisms, how many will you have after 3 hours, assuming that you have an abundant supply of all required nutrients?

Answer 1

To solve such problems, you first need to find the number of times the organism is going to divide in the given amount of time.
The generation time of the organism is 30 minutes, that means 30 minutes interval is required for the population to produce 4 progenies.
60/30 is 2
So the population would divide twice every hour.
If the organism grows for three hours, each would divide 2 times every hour x 3 hours = 6 times.

Next, calculate the number of organisms produced in the given time period.
for this you can use the equation
N = N_o 4^{^n}
where N is the number of organisms at any given generation n,
N_o is the initial number of organisms present, and
  n is the number of generations.
This is simply the permutaion of the number of possibilities if 4 progenies are produced every time it divides. If like in bacterias it produced 2 progenies every time it divided the permutation would have been 2^{^n} .  

So with this formula,
Number of organisms at the beginning = 10
number of divisions = 6
10 x 4^6 = 40,960 organisms at the end of three hours.