Question

A population of 100 individuals has a doubling time of 25 years. what size will this population be in 100 years?
A. 100
B. 400
C. 1600
D. 3200

Answer 1

The doubling time of a population is the time taken by a given population to double its size by growing at a constant rate. The formula for calculating the estimated population is $b = \dfrac{B}{{{2^n}}}$

Complete answer:
For the given question, in a population of a hundred individuals, it is given that the doubling time is 25 years.
Formula as mentioned, $b = \dfrac{B}{{{2^n}}}$
Here, b= expected population
B=present population and
n is the number of generations
By applying the values provided in the question, at first, we have to calculate out the number of generations which turns out to be $\dfrac{{100}}{{25}} = 4$
Now, the question asks us to calculate the population size after 100 years. Thus, to calculate the expected population in 100 years, we put the values in the mentioned formula;$b = \dfrac{{100}}{{{2^4}}}$
which implies that b= 1600.
Thus after 100 years, the population size will be 1600.

Hence, the correct answer is option (C).

Note: The doubling time for a population that is growing exponentially can also be calculated. For this purpose, there is a rule of 70. The doubling time is represented in years and is calculated by dividing 70 rates by the annual growth. This is called the Rule of 70. The annual growth rate of the population here is thus, $2.8\%$.