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

The population of rabbits was 4702 in year 1872.

What is an algebraic expression?

An algebraic expression is consists of variables, numbers with various mathematical operations,

Given that,

Total rabbit imported from England = 24

Also, annual growth rate of increasing the rabbit = 140 %  

To find the number of rabbits in 13 years from 1859 to 1872,

Use formula,

$S_n = a_1 (1-r^n) / r-1,$

Here Sₙ is required number of rabbits, a₁ is the initial number of rabbits, and r= 1.4 and n = 13 years

Sₙ = 24(1 - 1.4¹³)/1-1.4

Sₙ  = 24 x 195.92

Sₙ = 4702.2

The population of rabbits was 4702 in year 1872.

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