Exponential Growth vs. Decay Flashcard

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. For example, if a population grows by 5% each year, it is experiencing exponential growth.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. For example, if a radioactive substance decays by 10% each year, it is experiencing exponential decay.

Front

Identify the general form of an exponential growth function.

Back

Front

Identify the general form of an exponential decay function.

Back

Front

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

Back

In an exponential function, the base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor. It determines how quickly the function increases or decreases.

Front

How can you determine if a function represents exponential growth or decay from its equation?

Back

If the base of the exponent is greater than 1, the function represents exponential growth. If the base is between 0 and 1, it represents exponential decay.

Front

What is the significance of the initial value 'a' in an exponential function?

Back

Front

How does the graph of an exponential growth function behave?

Back

The graph of an exponential growth function rises steeply as x increases, showing a rapid increase in value.

Front

How does the graph of an exponential decay function behave?

Back

The graph of an exponential decay function falls steeply as x increases, showing a rapid decrease in value.

Front

What is an example of a real-world situation that demonstrates exponential growth?

Back

An example of exponential growth is the increase in a population of bacteria that doubles every hour.