There are 20 parrots at the animal sanctuary. Their population is increasing at a rate of 15% per year. There are also 24 snakes at the sanctuary. Each year 4 more snakes are born.

Part A: Write functions to represent the numbers of parrots and snakes at the sanctuary throughout the years.

Part B: How many parrots are at the sanctuary after 10 years? How many snakes are at the sanctuary after the same number of years? Assume there are no deaths to the animals during this time.

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

For the answer to the questions above,

A) Parrots are following a Geometric Progression of 15% increase.

20 (1.15), 20 (1.15) ², 20 (1.15) ³,

Function = 20 (1.15) ^n Where n is at the end of year, n = 1, 2, 3, ...

Snakes are increasing by 4.

28, 32, 36, ...

Function = 24 + 4n n = number of end year, n = 1, 2, 3, ...

B) After 10 years:

Parrot = 20 (1.15) ¹⁰ = 80.91115471

Snakes = 24 + 4 (10) = 64

C) After what time they are the same:

We use trial and error:

Test: n 20 (1.15^n) (24 + 4n)

1 23 28

2 26.45 32

3 30.41 36

4 34.98 40

5 40.23 44

6 46.26 48

7 53.20 52

8 61.18 56

9 70.36 60

After year 7, the Parrots increases far more.

At year 7 they are roughly the same.