Bacterial Population Estimation

An experimental scientific study has created a new species of bacteria in the laboratory. These bacteria have a particular life cycle. Each adult bacterium takes 3 days to divide and give rise to two new bacteria, and a newborn bacterium reaches adulthood in 1 day.

However, the bacteria are not synchronized with each other in terms of their division cycle.

Given an initial number of adult bacteria and a certain number of days, you need to determine the total number of bacteria in the population after that number of days.

If a bacteria has an internal counter of 3

• After one day it will be 2
• After another day it will be 1
• After one more day it will be 0
• After yet another day it will be 3 again, and another two new bacterias will be born with a counter of 4

As observed, an adult bacteria resets its counter to 3, while a newborn bacteria starts at 4 (due to taking a day to reach adulthood).

Then, if we have an initial state of 5 bacterias:

[2, 3, 3, 1, 2]

After 8 days, we will have an iteration as follows:

Initial state:    2,3,3,1,2
After  1 day:     1,2,2,0,1
After  2 days:    0,1,1,3,0,4,4
After  3 days:    3,0,0,2,3,3,3,4,4,4,4
After  4 days:    2,3,3,1,2,2,2,3,3,3,3,4,4,4,4
After  5 days:    1,2,2,0,1,1,1,2,2,2,2,3,3,3,3
After  6 days:    0,1,1,3,0,0,0,1,1,1,1,2,2,2,2,4,4
After  7 days:    3,0,0,2,3,3,3,0,0,0,0,1,1,1,1,3,3,4,4,4,4,4,4,4,4
After  8 days:    2,3,3,1,2,2,2,3,3,3,3,0,0,0,0,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4

Also, on day 8, we have a total of 37 bacterias, and after 60 days we would have a total of 7301991 bacterias

Notes:

• The initial number of adult bacteria is provided as the argument bacterias.
• The number of days is provided as the argument days.
• Feel free to choose the technology stack with which you feel most comfortable

Challenge

• Build a function to calculate the final number of bacteria produced from an initial set of bacteria after n days (the value of n is passed as an argument).
• Build an API to provide this tool to all biologists worldwide through the internet for many different initial sets of bacteria.
• This API should provide a method to configure a new bacterial strain with different maturation periods (days needed to reach adulthood), life expectancy, and reproduction rate (how many new bacteria are produced in each cell subdivision).
• The function must be efficient enough to simulate scenarios of up to 1000 days.
• Provide instructions to run and test your solution

There is no need to deploy the API on a real server.

Please send the public repository link with the solution to this challenge to joel@kwema.co or grant access to your GitHub repository to the GitHub user "joelibaceta".

Bonus

• Adhere to REST recommendations.
• Provide documentation and comments for code and API specification.
• Implement testing, such as unit testing.
• Implement proper error handling for user input mistakes.
• Consider the algorithm's complexity order.