Ohio Assessments for Educators (OAE) Mathematics Practice Exam

How is the rate represented in exponential growth formulas?

1. As ‘a’

2. As ‘r’

3. As ‘x’

4. As ‘e’

The correct answer is: As ‘r’

In the context of exponential growth formulas, the rate of growth is commonly represented by the symbol 'r'. This symbol is integral to the exponential growth model, which is typically expressed in the form \(N(t) = N_0 e^{rt}\), where \(N(t)\) is the amount at time \(t\), \(N_0\) is the initial amount, \(e\) is the base of the natural logarithm, and 'r' indicates the growth rate. The growth rate 'r' can be interpreted as the proportional increase in the quantity per unit of time, making it a crucial component in understanding how quickly the quantity grows over time. For example, a higher value of 'r' signifies a faster rate of growth, while a lower value indicates a slower rate. The other symbols mentioned hold different significance within mathematics. The symbol 'a' often represents an initial value or constant, 'x' frequently denotes the variable in equations or functions, and 'e' is specifically the base of the natural logarithm, which is used in exponential functions but does not represent the growth rate itself. Understanding the role of 'r' in these equations is essential for analyzing and predicting behaviors in exponential growth scenarios.