Exponential Growth and Decay Word Problems

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

Front

Define the growth rate (r) in an exponential function.

Back

The growth rate (r) is the percentage increase per time period in an exponential function, often expressed as a decimal.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the amount after time t, P 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 A = P(1 - r)^t, where A is the amount after time t, P 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 A = P(1 + r)^t, substituting P for the initial investment, r for the growth rate, and t for the number of years.

Front

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

Back

Use the formula A = P(1 - r)^t, substituting P for the initial value, r for the decay rate, and t for the number of years.

Front

What does a decay rate of 15% mean in an exponential decay model?

Back

It means that each year, the value decreases by 15% of its value from the previous year.

Tags

CCSS.HSF-IF.C.8B

Front

If a quantity decreases by 5% each year, what is the decay factor?

Back

The decay factor is 0.95, calculated as 1 - 0.05.

Tags

CCSS.HSF-LE.A.1C

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B