Exponential Growth and Decay Word Problems

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 process of reducing an amount by a consistent percentage rate over a period of time, leading to a decrease that slows down as the quantity decreases.

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate future value in exponential growth?

Back

Future Value = Present Value * (1 + growth rate)^number of periods.

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate future value in exponential decay?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for calculating percentage decrease?

Back

Percentage Decrease = (Original Value - New Value) / Original Value * 100.

Tags

CCSS.7.EE.A.1

Front

What is the formula for calculating percentage increase?

Back

Percentage Increase = (New Value - Original Value) / Original Value * 100.

Tags

CCSS.6.RP.A.3C

Front

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

Back

The decay factor is 0.95 (1 - 0.05).

Tags

CCSS.HSF-LE.A.1C

Front

If a quantity increases by 15% each year, what is the growth factor?

Back

The growth factor is 1.15 (1 + 0.15).

Tags

CCSS.HSF-LE.A.1C

Front

What is the significance of rounding in exponential problems?

Back

Rounding is important to provide a practical and usable answer, especially in real-world applications.

Front

How does compounding affect exponential growth?

Back

Compounding leads to exponential growth because the growth in each period is based on the total amount from the previous period.