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 at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

What is the general formula for exponential growth?

Back

The general formula is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the general formula for exponential decay?

Back

The general formula is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

How can you identify an exponential function from a table of values?

Back

If the ratio of consecutive values is constant, the function is exponential.

Front

How can you identify an exponential function from a graph?

Back

An exponential graph shows a curve that rises or falls sharply, rather than a straight line.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value.

Front

What does the base of an exponential function represent?

Back

The base indicates the growth factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is a common real-world example of exponential growth?

Back

Population growth is a common example, where the number of individuals increases rapidly over time.

Front

What is a common real-world example of exponential decay?

Back

Radioactive decay is a common example, where the quantity of a substance decreases over time.