Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which of the following represents the formula for an exponential growth function?

1. f(x) = a(1 + r)^x

2. f(x) = a(1 - r)^x

3. f(x) = ae^(rt)

4. f(x) = a + r/x

The correct answer is: f(x) = a(1 + r)^x

The formula representing exponential growth is characterized by a base raised to a power, which indicates how a quantity increases over time due to a constant growth rate. Option A, \( f(x) = a(1 + r)^x \), is correct because it illustrates exponential growth where \( a \) is the initial amount, \( r \) is the growth rate, and \( x \) represents time or the number of periods. In this formula, the term \( (1 + r) \) signifies that each time period, the quantity increases by a fixed percentage \( r \) from its previous value. This compounding effect leads to exponential growth, where increases become more substantial over time as the growth builds on itself. The other options represent different mathematical concepts or types of growth. For instance, option B indicates exponential decay since it contains \( (1 - r) \), leading to a decrease in value over time rather than an increase. Option C, which uses the natural exponential function \( e \), also describes a form of exponential growth, but it is specifically for continuous growth rather than discrete time intervals. Option D shows a linear relationship, which doesn’t account for percentage growth and therefore does not represent exponential growth. Thus, option A correctly