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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.8B

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.

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What is a real-world example of exponential decay?

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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?

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