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 decrease in a quantity where the rate of decrease is proportional to its current value, resulting in a decline that slows over time.

Tags

CCSS.HSF-IF.C.8B

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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.

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What does the base in an exponential function represent?

Back

The base represents the growth (if greater than 1) or decay (if between 0 and 1) factor applied to the initial amount.

Tags

CCSS.HSF-IF.C.8B

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If a population decreases by 1.5% per year, what is the decay rate in decimal form?

Back

The decay rate in decimal form is 0.015.

Tags

CCSS.HSF-LE.A.1C

Front

What is the significance of the initial value in an exponential function?

Back

The initial value represents the starting quantity before any growth or decay occurs.

Tags

CCSS.HSF-IF.C.8B

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How can you determine the number of years for a population to reach a certain size using an exponential function?

Back

You can solve for 't' in the exponential equation by rearranging it to isolate 't'.

Tags

CCSS.HSF.LE.A.4

Front

What is the difference between linear and exponential functions?

Back

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