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. F<span>unctions to represent the number of alligators and crocodiles in the swamp throughout the years. </span><span>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*(</span><span>20+0.25*20)+....+0.25*number of alligators in year N-1 For the crocodiles we can write: </span>25+(25+10)+(25+10)+10+....<span>number of alligators in year N-1+10
</span><span>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) </span>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.<span>25*20))) Crocodiles: </span><span>25+(25+10)+((25+10)+10)+...=25+35+45+55+65=225 </span>