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)

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:

According to the above mentioned statement the function for representing the number of alligators and crocodiles in the swap throughout the year is:

Alligators = y=20(1.25)^x (x represents years)

crocodiles: y=10x+25

Part B:

Number of alligators after 4 years in the swap = y=20(1.25)^x

Number of alligators after 4 years in the swap = y=20(1.25)^4

Number of alligators after 4 years in the swap=48.82

This shows that about 48 to 49 alligators will be there in the swap after 4 year

Number of crocodiles after 4 years in the swap = y= 10(4)+25 = 65

Part C:

We will use the graph method to solve this part:

After approximately 7 years, the number of animals of each type will be the same, 95.