Chapter 46, Problem 1QC

Summary Introduction

To determine:

The per capita growth rate if the size of population triples in a year.

Introduction:

The change in the population size per unit of time divided by the number of individuals at the start is known as the per capita growth rate. It is denoted by $\text{r}$.

${\text{r=(ΔN/Δt)/N}}_{\text{1}}$

Explanation of Solution

If the size of a population triple in a year, then the per capita growth will be:

Here, the change in time ( $\text{Δt}$) is $\text{1}$ year.

So, ${\text{r=ΔN/N}}_{\text{1}}$

Let the starting population is $\text{x}$, then after $\text{1}$ year as the size is tripled, the size will be $\text{3x}$.

Therefore, $\text{ΔN=3x-x}$ or $\text{2x}$.

So, $\text{r=2x/x}$ or $\text{2}$

Conclusion

If the population triples in size in a year, then the per capita growth rate will be equal to $\text{2}$.