Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth that accelerates over time.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Front

Provide an example of a sequence that represents exponential growth.

Back

An example of exponential growth is the sequence 2, 4, 8, 16, 32, ... where each term is multiplied by 2.

Front

Provide an example of a sequence that represents exponential decay.

Back

An example of exponential decay is the sequence 100, 50, 25, 12.5, ... where each term is halved.

Front

What is the general formula for exponential growth?

Back

The general formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'k' is the growth rate, and 't' is time.

Front

What is the general formula for exponential decay?

Back

The general formula for exponential decay is f(t) = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay rate, and 't' is time.

Front

How do you identify exponential growth on a graph?

Back

Exponential growth on a graph is identified by a curve that rises steeply and continuously increases as it moves to the right.

Front

How do you identify exponential decay on a graph?

Back

Exponential decay on a graph is identified by a curve that falls steeply and continuously decreases as it moves to the right.

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the growth or decay factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept of an exponential function represents the initial value of the quantity before any growth or decay occurs.