In the year 1859, Thomas Austin imported 24 rabbits from England to his property in Australia for sport hunting. Australia has mild winters with no natural predators

Question

In the year 1859, Thomas Austin imported 24 rabbits from England to his property in Australia for sport hunting. Australia has mild winters with no natural predators, limited industrial development, and plentiful vegetation. Healthy lady bunnies can produce ten litters per year, and bunny colonies spread at a rate of 80 miles per year, covering the continent by 1890. Estimate the population of bunnies in the year 1872 or n = 13 given an annual growth rate of 140% or r = 1.4. Round to whole number.

Hint: Use Sn = a1 (1-r^n) / 1 - r

Answer 1

Geometric growth is illustrated using the following formula:

S_n = a(1 - rⁿ)

1 - r

where:

1. a = 24, the initial number of rabbits
2. r = 1.4, the growth rate of 140% /year
3. n = 13, the number of years from 1859 to 1872

Plugging in the values and solving for S_n we get:

S_n = 4,702, which is the estimated rabbit population in the year 1872.