4.2 Exp Growth and Decay Applications

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to rapid increases as time goes on.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to rapid decreases as time goes on.

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CCSS.HSF-IF.C.8B

Front

How can you identify exponential growth or decay from a function?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

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CCSS.HSF-IF.C.8B

Front

What does the variable 'a' represent in the function A = a(b)^t?

Back

The variable 'a' represents the initial amount or starting value in the exponential function.

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CCSS.HSF.LE.B.5

Front

In the function A = 1200(0.85)^6, what does 0.85 represent?

Back

The value 0.85 represents the decay factor, indicating a 15% decrease each time period.

Tags

CCSS.HSF.LE.B.5

Front

What is the formula for calculating the population after a certain number of years with decay?

Back

The formula is A = P(1 - r)^t, where P is the initial population, r is the rate of decay, and t is the time in years.

Front

If a population decreases by 6% per year, what is the decay factor?

Back

The decay factor is 0.94, calculated as 1 - 0.06.

Tags

CCSS.HSF-LE.A.1C

Front

What is the population of fish after 10 years if it starts at 8000 and decreases by 6% per year?

Back

The population after 10 years is approximately 4309.

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CCSS.HSF-LE.A.1C

Front

What does the term 'half-life' mean in the context of exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value.

Front

How do you convert a percentage decrease to a decay factor?

Back

Subtract the percentage decrease from 1. For example, a 20% decrease gives a decay factor of 0.80.

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CCSS.HSF.BF.A.2