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 decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

How do you calculate future value in exponential growth?

Back

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

Front

How do you calculate future value in 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 10% interest rate compounded annually?

Back

It means that each year, the interest earned is added to the principal, and the next year's interest is calculated on the new total.

Front

What is the significance of compounding in finance?

Back

Compounding allows interest to be earned on previously earned interest, leading to exponential growth of savings or investments over time.