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? Justify your answer mathematically. (4 points)

Answer 1

Explanation:

Part A -

parrots: f(x) = 20(1.15)^x

Snakes: f(x) = 24 + 4x

Part B - there would be approximately 81 parrots and 64 snakes after 10 years and no deaths!

Part C - 20(1.15)^x = 4x + 24

x = 6.63 years they will be the same

Answer 2

A.
y = 20(1.15)^x.....parrots
y = 4x + 24.....snakes

B. after 10 yrs
y = 20(1.15^10)
y = 20(4.05)
y = 81 parrots

y = 4(10) + 24
y = 40 + 24
y = 64 snakes

C.
20(1.15)^x = 4x + 24
x = 6.63 years they will be the same