Open Note Flashcard: Exponential Functions (growth/decay)

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

Front

What characterizes exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to a rapid increase over time.

Front

What characterizes exponential decay?

Back

Exponential decay occurs when the decrease rate of a value is proportional to its current value, leading to a rapid decrease over time.

Front

How can you identify exponential growth in a graph?

Back

In a graph, exponential growth is represented by a curve that rises steeply as x increases.

Front

How can you identify exponential decay in a graph?

Back

In a graph, exponential decay is represented by a curve that falls steeply as x increases.

Front

What is the general form of an exponential decay equation?

Back

The general form is A = A0 * (1 - r)^t, where A0 is the initial amount, r is the decay rate, and t is time.

Front

What is the general form of an exponential growth equation?

Back

The general form is A = A0 * (1 + r)^t, where A0 is the initial amount, r is the growth rate, and t is time.

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' represents the growth (b > 1) or decay (0 < b < 1) factor in the function.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases rapidly.

Front

What does it mean if an exponential function has a base less than 1?

Back

If the base is less than 1, the function represents exponential decay.