Question

There are 20 parrots at the animal sanctuary. Their population is increasing by 5 parrots each year. There are also 24 snakes at the sanctuary. Each year 4 more snakes are born. Part A: Write a function to represent the numbers of parrots at the sanctuary throughout the years. (6 points) Part B: Write a function to represent the numbers of snakes at the sanctuary throughout the years, (6 points) Part C: 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. (6 points) Part D: After approximately how many years is the number of parrots and snakes the same? Justify your answer mathematically. (7 points)

Answer 1

Part A

Initial population of parrot in the animal sanctuary = 20 parrots

The population is increasing by 5 parrots per year.

let

number of years = x

y = population of parrot

The function can be represented as

$y=5x+20$

Part B.

Initial population of snake in the sanctuary = 24

Each year 4 more snakes are born

let

number of year = x

y = population of the snake

The function can be represented below

$y=24+4x$

Part C

Number of parrot in 10 years

$\begin{gathered} y=5x+20 \\ y=5(10)+20 \\ y=50+20=70 \\ Number\text{ of parrot in 10 years = 70} \end{gathered}$

Number of snakes in 10 years

$\begin{gathered} y=4x+24 \\ y=4(10)+24 \\ y=40+24=64 \\ Number\text{ of snakes in 10 years = }64 \end{gathered}$

Part D

The number of year where the number of parrot and snakes are the same can be calculated below

$\begin{gathered} 5x+20=4x+24 \\ 5x-4x=24-20 \\ x=4 \end{gathered}$

The snakes and the parrot will be equal in population after 4 years time.