Exponential Growth & Decay

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a fixed percentage over a period of time, leading to rapid increases as the base amount grows.

Tags

CCSS.HSF-LE.A.1A

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to rapid decreases as the base amount shrinks.

Tags

CCSS.HSF-IF.C.8B

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What is the 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 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

How do you calculate the population after a certain number of years with decay?

Back

Use the formula: Final Population = Initial Population * (1 - decay rate)^number of years.

Tags

CCSS.HSF.LE.A.4

Front

How do you calculate the population after a certain number of years with growth?

Back

Use the formula: Final Population = Initial Population * (1 + growth rate)^number of years.

Tags

CCSS.HSF-LE.A.1C

Front

What does a growth rate of 35% mean?

Back

It means that the quantity increases by 35% of its current value each year.

Tags

CCSS.HSF-IF.C.8B

Front

What does a decay rate of 6% mean?

Back

It means that the quantity decreases by 6% of its current value each year.

Tags

CCSS.HSF-IF.C.8B

Front

If a population of 4,000 grows at 25% per month, how do you find the population after 4 months?

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Use the formula: Final Population = 4000 * (1 + 0.25)^4.

Tags

CCSS.HSF-LE.A.1C

Front

What is the difference between linear growth and exponential growth?

Back

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