Question

In 1926, five pigs were also introduced into the 100 Acre Woods. Dr. Robin decided to study pigs in the 100 Acre Woods in 1930. At that time, there were 100 pigs in the Woods. Assuming that this is nowhere close to the carrying capacity of pigs in the 100 Acre Woods, what is the geometric rate of growth of pigs in the 100 Acre Woods (report to two decimal places)?

Answer 1

Given, the population of pigs are increasing geometrically (or exponentially) over the period of 4 years.

Basic equation for exponential growth is:

Y_t = Y₀(1+r)^t

where, Y₀ is initial population,

r is growth rate (in percentage)

t is the number of years

Solving for r, r = (Y_t/Y₀)^(1/t) - 1

So, as per the information given, initial population = 5

Time in years = 4

Population after 4 years = 100

r = (100/5)^(1/4) - 1

r = 20^(0.25) - 1

r = 2.115 - 1

r = 1.115

Hence, the growth rate of pig population is 111.47 percent per year.