Exponential Growth & Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of 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 of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Tags

CCSS.HSF-IF.C.8B

Front

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 future value of an investment with exponential growth?

Back

Use the formula: Future Value = Present Value * (1 + growth rate)^number of years.

Front

How do you calculate the remaining value of an asset with exponential decay?

Back

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

Front

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

Back

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

Tags

CCSS.HSF-LE.A.1A

Front

What is a common example of exponential decay in real life?

Back

A common example is radioactive decay, where unstable atoms lose energy and mass over time.

Front

If a population of 1000 increases by 20% each year, how many will there be after 3 years?

Back

There will be approximately 1820 individuals after 3 years.

Tags

CCSS.HSF-LE.A.1C

Front

If a car depreciates in value by 15% each year, what will its value be after 4 years if it starts at $20,000?

Back

The car will be worth approximately $8,000 after 4 years.

Tags

CCSS.HSF.BF.A.2