Question

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?

Answer 1

Part A. Functions. Parrots: it is a geometric progression: first year, 20 parrots; second year, 20 * 1.15; third year 20 * 1.15^2, fourth year, 20*1.15^3 => P(n) = 20 (1.15) ^ (n -1). Snakes: it is an arithmetic progression: first year, 24 snakes; second year, 24 + 4 snake; third year, 24 * 4(2) => S(n) = 20 + 4(n-1). Part B. Parrots after 10 years = P(10) = 20(1.15)^9 = 70 Parrots. Snakes after 10 years = S(10) = 20 + 4 (10-1) = 56.