USA Biology Olympiad (USABO) Practice Exam

In a population with 34 births and 25 deaths, what is the value of r?

1. 0.25

2. 0.09

3. 0.15

4. 0.50

The correct answer is: 0.09

To find the value of r, which represents the intrinsic rate of population growth, we use the formula: \[ r = \frac{B - D}{N} \] where: - \( B \) is the number of births, - \( D \) is the number of deaths, and - \( N \) is the total population size (assumed to be constant during the time frame considered). In this scenario, we have 34 births and 25 deaths. First, we need to determine the net change in population, which is calculated as follows: \[ B - D = 34 - 25 = 9 \] Next, we typically need the total population size to calculate \( r \). However, since it is not given, we can express \( r \) in proportional form by assuming \( N \) (the total population size) is the average population size for simplicity. We can take the net change in population (9) and then determine \( r \) as a fraction of this average population size. In practice, if we make the assumption about the population size or if it is implicitly considered to be an average number over a relevant time frame, we can draw conclusions directly from the net change.