Question

If a population exhibits discrete growth, and doubles in size over 14 years, what is the value for the finite rate of increase (given 1 generation per 2 years)?  Given that the size starts at 40, what would the size of this population be in 30 years

Answer 1

Problem statement:- Growth characteristics of a population is given. Based on this we have to answer few questions.

Given:-It is given that a population exhibits a discrete growth. Also it is provided that the population doubles in 14 years. Based on this information we have to answer few questions.

Solution:- Growth of a population at a particular rate can be mathematically modelled to follow a compounded growth at a particular rate .

Let "r" be the growth rate.

Let "p" be the initial population,

Let "y" be the current year. and P(y) be the population in year "y".

Now the population growth can be modelled as,

P(y)=((1+(r/100))^(y-initial year))_*p

It is given population doubles in 14 years.

= 2*p=(1+(r/100))^14*p

2=(1+(r/100))^14

Solving for "r" we get r=5.0756%

We use the same approach to compute the population after 30 years.

P(after30 years)=((1+(5.0756/100))^30)_*40

P(after30 years)=(4.4163)_*40

P(after 30 years)= 176.65