There are 20 alligators in the swamp. each year, the number of alligators increases by 25%. there are 25 crocodiles in the swamp. each year, 10 new crocodiles join the swamp. part a: write functions to represent the number of alligators and crocodiles in the swamp throughout the years. (4 points) part b: how many alligators are in the swamp after 4 years? how many crocodiles are in the swamp after the same number of years? (2 points) part c: after approximately how many years is the number of alligators and crocodiles the same? justify your answer mathematically. (4 points)

A. Functions to represent the number of alligators and crocodiles in the swamp throughout the years.
We know that there are 20 alligators in the swamp and that each year, the number of alligators increases by 25%.So, if this year the number of alligators is 20, the next year it will be 20+25%of 20=20+0.25*20
In the year N from now the number of alligators will be: 20+(0.25*20)+0.25*(20+0.25*20)++0.25*number of alligators in year N-1
For the crocodiles we can write: 25+(25+10)+(25+10)+10+number of alligators in year N-1+10

Part B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years? (2 points) 
In 4 years there will be: 
Alligators:20+0.25*20+0.25*(20+0.25*20)+0.25*(0.25*(20+0.25*20))+0.25*(0.25*(0.25*(20+0.25*20)))
Crocodiles: 25+(25+10)+((25+10)+10)+...=25+35+45+55+65=225