5.2 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.

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.

Front

How do you calculate future value with exponential growth?

Back

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

Front

How do you calculate future value with exponential decay?

Back

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

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time in years.

Front

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

Back

The decay factor is 0.95 (1 - 0.05).

Front

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

Back

The growth factor is 1.15 (1 + 0.15).

Front

What does it mean to round to the nearest whole number?

Back

Rounding to the nearest whole number means adjusting a decimal number to the closest integer.

Front

How do you interpret a percentage decrease in a real-world context?

Back

A percentage decrease indicates how much a quantity has reduced compared to its original value, often used to analyze trends over time.

Front

How do you interpret a percentage increase in a real-world context?

Back

A percentage increase indicates how much a quantity has grown compared to its original value, often used to analyze trends over time.