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 a rapid increase. Example: Population 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. Example: Radioactive decay.

Front

How can you identify exponential growth on a graph?

Back

Exponential growth graphs rise steeply and curve upwards as they progress from left to right.

Front

How can you identify exponential decay on a graph?

Back

Exponential decay graphs fall steeply and curve downwards as they progress from left to right.

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

What does the variable 'r' represent in exponential functions?

Back

In exponential functions, 'r' represents the rate of growth (for growth) or decay (for decay) expressed as a decimal.

Front

What is a real-world example of exponential growth?

Back

A real-world example of exponential growth is the spread of a viral infection, where each infected person can infect multiple others.

Front

What is a real-world example of exponential decay?

Back

A real-world example of exponential decay is the decrease in the amount of a radioactive substance over time.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much larger values over time.