Exponential Growth and Decay Word Problems

Front

What is exponential decay?

Back

Exponential decay refers to a decrease in a quantity by a consistent percentage over a period of time, resulting in a rapid decline.

Front

How do you calculate the future value of an investment with compound interest?

Back

Future Value = Present Value * (1 + interest rate)^number of years.

Front

What is the formula for exponential growth?

Back

Exponential Growth = Initial Amount * (1 + growth rate)^time.

Front

If a population decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.80 (1 - 0.20).

Front

How do you find the number of subscribers after a certain number of years with a decay rate?

Back

Use the formula: Future Subscribers = Initial Subscribers * (1 - decay rate)^number of years.

Front

What does it mean for a quantity to grow by 15% each year?

Back

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

Front

If a savings account has an interest rate of 5% compounded annually, how much will $100 be worth in 2 years?

Back

Future Value = 100 * (1 + 0.05)^2 = $110.25.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage.

Front

How do you round a number to the nearest whole number?

Back

If the decimal is 0.5 or higher, round up; if it's less than 0.5, round down.

Front

What is the initial population in a decay problem?

Back

The initial population is the starting amount before any decay occurs.