Now assume that rabbits reach sexual maturity instantly afte

Now, assume that rabbits reach sexual maturity instantly after being born and all can reproduce continuously (generations overlap). If each pair has 4 offspring and both parents die by the end of the year:

a)How many rabbits are there after 10 years?

b)How many rabbits are there after 25 years?

Solution

It is given that there are 4 births every year in the population. Before the death of parents at the end of year the population will be 6. Now we need to calulate number of rabbits or Nt after 10 years and 25 years.

First calculating birth rate:

Birth rate = 4/6= 0.667

Now calculating death rate:

Birth rate = 2/6= 0.333

Now calculating r,

r = birth rate - death rate

r = 0.667- 0.333

r = 0.334

t= 10

Now putting all values in the equation of Nt you can easily calculate the number of rabbits in 10 years as well as 25 years.

For 10 years Nt can be calculated as:

Nt = No e ^rt

Nt = 6 e ^{(0.334) (10)}

For 25 years Nt can be calculated as:

Nt = No e ^rt

Nt = 6 e ^{(0.334) (25)}