Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time, leading to a decrease that slows down as the quantity decreases.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.8B

Front

How do you convert a percentage to a decimal for calculations?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 14.9% becomes 0.149.

Front

What does the term 'initial value' refer to in exponential functions?

Back

The initial value is the starting amount before any growth or decay occurs, represented by 'a' in the formulas.

Tags

CCSS.HSF.LE.B.5

Front

What is the significance of the base in exponential functions?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

How can you determine the range of an exponential function?

Back

The range of an exponential function is typically y > 0 for growth and y ≥ 0 for decay, as the output cannot be negative.

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What is a real-world example of exponential growth?

Back

A common example is population growth, where the number of individuals increases rapidly as the population grows.

Tags

CCSS.HSF-LE.A.1A

Front

What is a real-world example of exponential decay?

Back

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