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.

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.

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.

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.

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.

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.

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.