Construct the recipe for a new probiotic

As a food researcher at large beverage company, you have been tasked with coming up with a secret formula for the next probiotic superfood: water kefir! At any point in time during the fermentation process, the water kefir solution can have four ingredients that react with each other: sugar water, acid, carbon dioxide, and the water kefir culture itself.

You know how each ingredient of the solution changes in one hour:

• 10% of the sugar water gets converted to acid, and another 15% is converted to the culture.
• 15% of the acid is converted to carbon dioxide, and 5% is converted to the culture.
• 45% of the carbon dioxide gets re-absorbed back into acid.
• The culture does not change into another state.

Given the initial solution contains 80% of sugar water and 20% of culture, find how many hours it will take for the concentration of sugar water to decrease to 11%, and save this as hours. Save the composition of ingredients at this time as the 1d numpy array composition, assuming the following ingredient's order:

1

composition_ingredient_order = ['sugar water', 'acid', 'co2', 'culture']

Your code snippet should define the following variables: