Exponential Growth & Decay

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What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay is the process by which a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general formula for exponential growth?

Back

The general formula for exponential growth 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 for exponential decay 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

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What does the y-intercept represent in an exponential function?

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The y-intercept represents the initial value of the function when time (t) is zero.

Tags

CCSS.HSF-IF.C.7E

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How can you identify exponential growth on a graph?

Back

Exponential growth is identified by a curve that rises steeply and continuously increases as it moves to the right.

Tags

CCSS.HSF-IF.C.7E

Front

How can you identify exponential decay on a graph?

Back

Exponential decay is identified by a curve that decreases rapidly and approaches zero as it moves to the right.

Tags

CCSS.HSF-IF.C.7E

Front

What is the significance of the base in an exponential function?

Back

The base of an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate the population after a certain time in exponential growth?

Back

To calculate the population after a certain time in exponential growth, use the formula y = a(1 + r)^t, substituting the initial population for 'a', the growth rate for 'r', and the time for 't'.

Tags

CCSS.HSF-LE.A.1A

Front

What is a common application of exponential growth in real life?

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A common application of exponential growth is in population studies, where populations can grow rapidly under ideal conditions.