Question

(05.03 HC)

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. (4 points)
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. (2 points)
Part C: After approximately how many years is the number of parrots and snakes the same? Justify your answer mathematically. (4 points)

Answer 1

Let P represent no of parrots and S represent no of snakes.
The parrots increase by 15% so at the end of each year, the population of P represented by nP is nP = (P + 0.15P).
4 new snakes are born every year so the population of S represented by nS is nS = S +(0.17S).
PART B
At end of 1st year, no of parrots will be 20+ (0.15 x 20) = 23 parrots
At end of 2nd year. there will be 23 +(0.15 x 23) = 26 parrots
At end of 3rd year there will be 26 + (0.15 x 26) = 30 parrots
At end of 4th year, there will be 30 + (0.15 x30) = 35 parrots
At end of 5th year, there will be 35 + (0.15 x 35) = 40 parrots
At the end of 6th year, there will be 40 + 0.15 x 40) = 46 parrots
At the end of 7th year, there will be 46 + (0.15 x 46) = 53 parrots
At the end of 8th year, there will be 53 + (0.15 x 53) = 61 parrots
At the end of 9th year, there will be 61 + (0.15 x 61) = 70 parrots
At the end of 10th year, there will be 70+ (0.15 x 70) = 81 parrots

Four more snakes are born each year, so at the end of 10 years 40 snakes would have been added and the population would then be (24 + 40) = 64 snakes.
PART C
After approximately 6 years, the population of parrots nP = P' + (0.15 x P')
where P' is the number of parrots at the beginning of the year. This will give a total parrot population of 46; similarly, a total of 6 x 4 = 24 new snakes would have been added to bring the total to (24 + 24) = 48 snakes.