Question

PLEASE HELP!! ASAP.

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)

Answer 1

Part A

Each year the number of alligators is 1.25 times the number the year before. Repeated multiplication by this value can be represented using an exponent. The equation for the number of alligators (a) as a function of the number of years (t) can be written as

... a(t) = 20·1.25^t

Each year, the number of crocodiles increases by 10. Repeated addition can be represented using multiplication. The equation for the number of crocodiles (c) as a function of the number of years (t) can be written as

... c(t) = 25 +10t

Part B

... a(4) = 20·1.25⁴ ≈ 48.83 ≈ 49

... c(4) = 25 +10·4 = 65

After 4 years, there are 49 alligators and 65 crocodiles.

Part C

You want t that solves a(t) = c(t). Such an equation cannot be solved algebraically, but it can be solved by any of a variety of other methods. My personal preference is for a graphical solution.

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

a(7) = 95.4

c(7) = 95

These numbers both round to 95.