How to calculate how long it will take for a number to reach the maximum using recursion?

Question

I'm writing a recursive function to analyze various species population growth over time. I have four parameters: The initial population of the species in the first year (a), the year where I want to see what the population will be in years to come (b), the growth rate in a percentage (c) and lastly the maximum amount of the certain species the environment can handle (d).

(Population growth formula I am using is (a * b-1 + c) * (a *b-1) * 1 - (a * b-1/d))

So far this is what I have:

def animal_growth(a,b,c,d):
    growth = (a * b-1 + c) * (a *b-1)
    max_growth = growth * 1 - (a * b-1/d)
    if a > 10000:
         return 
    else:
         return max_growth 

 animal_growth(200,20,0.05,5000)

So in the above example, I'm looking to find how long it will take for the animal population to exceed 5000 at a growth rate of 5% per 'year', long with what that population will be in 20 years, starting with the population at 200.

I was hoping to get a console output something like:

  8.4 # how long it will take to exceed 5000 
  6000 # the population after 20 years 
  # neither of these might be correct so if there are different answers no worries

I'm stuck on the recursive end of things, the formulas and math I understand.

Thank you for your help!

Answer 1

The function you need is something like this:

def animal_growth(growth,year,rate,max_growth, years=0):
    growth = (growth + (growth*rate))
    if growth < max_growth:
        years += 1
        if years == year:
            print (growth)
        return animal_growth(growth, year, rate, max_growth, years) 
    else:
        return (1 + years) 

    print(animal_growth(200,20,0.05,5000))

Answer 2

I think you should create 2 separate function, one to calculate the years it take to grow to a certain number, one to calculate how much it could grow given a certain number of years

def number_of_years_to_grow(initial, rate, max_growth):
    growth = initial * (1 + rate)
    if (growth <= max_growth):
        return 1 + animal_growth(growth, rate, max_growth)
    else:
        return 1 # or return 0 (depending on whether you want to include the year where it exceed the maximum number or not)

def population_growth(initial, years, rate):
    return initial * ((1 + rate) ** years)

print(number_of_years_to_grow(200, 20, 0.05))
print(animal_growth(200, 0.05, 5000))

Also, additional tips, please use a meaningful variable name for readability purpose.