Exponential Growth & 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 the formula for Exponential Growth?

Back

The formula is: P(t) = P0 * (1 + r)^t, where P(t) is the future population, P0 is the initial population, r is the growth rate, and t is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is Exponential Decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a decrease at a decreasing rate over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for Exponential Decay?

Back

The formula is: P(t) = P0 * (1 - r)^t, where P(t) is the future value, P0 is the initial value, r is the decay rate, and t is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is a Growth Factor?

Back

The growth factor is the amount by which a quantity increases in one time period, calculated as (1 + r) for growth.

Tags

CCSS.HSF-IF.C.8B

Front

What is a Decay Factor?

Back

The decay factor is the amount by which a quantity decreases in one time period, calculated as (1 - r) for decay.

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 periods.

Front

How do you calculate the future value of an investment with exponential decay?

Back

Use the formula: Future Value = Present Value * (1 - decay rate)^number of periods.

Front

What is the significance of the rate in exponential functions?

Back

The rate determines how quickly the quantity grows or decays; a higher rate results in faster changes.

Tags

CCSS.HSF-IF.C.8B

Front

How does compounding affect exponential growth?

Back

Compounding leads to exponential growth because the growth builds on itself, increasing the base amount each period.