A flesh eating breed of dodo bird was introduced onto a smal

A flesh eating breed of dodo bird was introduced onto a small island with an initial population of 190 birds, and scientists estimate that the bird population is doubling every year.

a) Find a function N that models the number of dodo birds after t years.

b) Estimate the bird population after 12 years

Solution

Since the population doubles every year, the population will be,

190, 380, 760, 1520,....

This represents a geometric series where

initial term, a = 190

common ratio, r = 380/190 (or) 760/380 (or) 1520/760 ... = 2.

(a) Population after t years, P(t) =t^th term of a geometric series = a(r^t-1) =190 (2^t-1) (where t=1,2,....)

(b) Population after 12 years = 190 (2^12-1) = 190(2¹¹) = 389120