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 B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years?

Part C: After approximately how many years is the number of alligators and crocodiles the same? Justify your answer mathematically.

Question

Mathematics

Downs

25 July, 09:00

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 B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years?

Part C: After approximately how many years is the number of alligators and crocodiles the same? Justify your answer mathematically.

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Answers (1)

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London · Answer 1

A)

A=20 (1.25^t)

C=25+10t

b)

A (4) = 20 (1.25^4) ≈48.82≈49 alligators to nearest whole alligator

C (4) = 25+10 (4) = 65 crocodiles.

c)

20 (1.25^t) = 25+10t

1.25^t=1.25+0.5t

t≈7