Exponential Growth and Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in 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 refers to the decrease in a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

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

Back

Future Value = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the formula for calculating population after a percentage decrease?

Back

Population after decrease = Initial Population * (1 - rate of decrease) ^ number of years.

Front

If a quantity decreases by 10% each year, what is the multiplier for each year?

Back

The multiplier is 0.90 (1 - 0.10).

Front

If a quantity increases by 10% each year, what is the multiplier for each year?

Back

The multiplier is 1.10 (1 + 0.10).

Front

What is the value of an item that depreciates by 18% each year if it starts at $1500?

Back

Value after 1 year = 1500 * (1 - 0.18) = $1230.

Front

How do you find the interest earned on a savings account with compound interest?

Back

Interest Earned = Future Value - Principal.

Front

What is the effective interest rate if the nominal rate is compounded annually?

Back

The effective interest rate is the same as the nominal rate when compounded annually.

Front

How do you round 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.