Question 1 A single breeding pair of rabbits is introduced t

Question 1 A single breeding pair of rabbits is introduced to Australia in 1900. Assume (for simplicity) that each pair can produce 4 offspring each year (2 male, 2 female). Also assume, that all births happen in the last hour of the last day each year and the parents die immediately after offspring are born.

a) How many rabbits are there after 10 years?

b) How many rabbits are there after 25 years?

If they have 20 offspring each year,

c) How many rabbits are there after 10 years?

d) How many rabbits are there after 25 years?

Solution

Number of rabbits at the begining = 2 ( 1 pair).

Nuber of rabbits produced each year by each pair = 4 ( 2 males & 2 females) ie 2 pairs.

Number of rabbits produced during first year will be , 4 (2 pairs) because parents die after the birth of their offsprings.

These 2 pairs will produce 8 rabbits (4 pairs) in the second year.

That means each year number of rabbit pairs become double.

Number of rabbits produced during third year = 16 ( 8 pairs).

(A) Therefore number of rabbits produced after 10 years will be =

(2)^10 pairs = (2×2×2×2×2×2×2×2×2×2 )pairs = 1024 pairs.

Therefore 1024 pairs of rabbit will be produced after 10 years.

(B) Number of rabbit pairs produced after 25 years will be

(2)^25 = 33,554,432.

If They have 20 offsprings each year.

Number of rabbits produced in the first year will be 20 (10 males and 10 females) ie 10 pairs.

These 10 pairs will breed and produce 200 rabbits (100 pairs) in second year.

That means number of rabbits increase by ten fold each year. (C) Therefore number of rabbits produced after 10 years will be

(10)^10 pairs = (10×10×10×10×10×10×10×10×10×10) = 10,000,000,000.

(D) Number of rabbits produced after 25 years will be

(10)^25 = 10,000,000,000,000,000,000,000,000.