Exponential growth vs decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to rapid increases as time progresses.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to rapid decreases as time progresses.

Front

What is the general formula for exponential growth?

Back

The 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 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 exponential growth on a graph?

Back

Exponential growth graphs rise steeply and curve upwards, indicating rapid increases.

Front

How can you identify exponential decay on a graph?

Back

Exponential decay graphs fall steeply and curve downwards, indicating rapid decreases.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What does a base greater than 1 indicate in an exponential function?

Back

A base greater than 1 indicates exponential growth.

Front

What does a base between 0 and 1 indicate in an exponential function?

Back

A base between 0 and 1 indicates exponential decay.

Front

If a population doubles every year, what type of growth is this?

Back

This is an example of exponential growth.