Question

The Metro Toronto Zoo has an endangered species called the Eastern cougar. A pair of cougars have a fecundity of 5 offspring per year where all offspring survive to reproductive age (2.5 per parent per generation).

1. Explain the type of growth
2. Calculate the number of cougars after 5 years and 9 years.

Answer 1

Initial number of cougars = 2

Number of cougars after 1 year = parents + offsprings = 2 + 5 = 7

Number of cougars after 2 year = number of individuals after 1 years + new offsprings = 7 + ( 7 × 2.5) = 24.5

Similarly,

Number of individuals after 3 years = 85.75

As we can see,

2, 7, 24.5, 85.75

This series is following the geometric possession with the constant ratio

7/2 = 24.5/7 = 85.75/24.5 = 3.5

Constant ratio = 3.5

a. The population size is increasing by the constant rate of 3.5 . Therefore, this is a GEOMETRIC GROWTH.

b. Number of cougars after 5 years

= Initial population × (constant rate)^5

= 2 × (3.5)^5 = 1,050.4375 or, 1,050.5

Number of cougars after 9 years

= Initial population × (constant rate)^9

= 2 × (3.5)^9 = 157,631.278 or, 157,631.3

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