Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What does the variable 'a' represent in population growth formulas?

1. Rate of growth

2. Current count

3. Initial population

4. Time period

The correct answer is: Initial population

In population growth formulas, the variable 'a' often represents the initial population size. This is the starting amount of individuals in a population before any growth occurs. Understanding this is crucial as it provides a baseline from which population changes can be measured over time. When analyzing population growth, typically modeled by equations such as the exponential growth formula \( P(t) = a \cdot e^{rt} \), the variable 'a' indicates how many individuals were present at the beginning of the observation period. This initial population size influences how quickly the population can grow, depending on the growth rate and time. By knowing the initial population, one can track changes over specified time periods, which are influenced by the growth rate and time variable. Thus, recognizing 'a' as the initial population size is essential in understanding overall population dynamics in these formulas.