Exponential Growth and Decay

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.

Front

What is exponential decay?

Back

Exponential decay is the process by which a quantity decreases by a fixed percentage over time, resulting in a rapid decrease as the quantity diminishes.

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 population of 1000 increases by 10% each year, what will it be after 3 years?

Back

Population after 3 years = 1000 × (1 + 0.10)^3 = 1331.

Front

What is the half-life of a substance?

Back

Half-life is the time required for a quantity to reduce to half its initial value, commonly used in radioactive decay.

Front

If a printer worth $5000 depreciates at 10% per year, what will it be worth after 5 years?

Back

Value after 5 years = 5000 × (1 - 0.10)^5 = $3051.57.

Front

What is the growth rate in the context of exponential growth?

Back

The growth rate is the percentage increase in a quantity over a specific period of time.

Front

What is the decay rate in the context of exponential decay?

Back

The decay rate is the percentage decrease in a quantity over a specific period of time.