Exponential Growth and Decay Word Problems

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 occurs when a quantity decreases by a fixed percentage over a period of time, leading to rapid decreases as the base amount shrinks.

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

How do you calculate the future value of an investment with exponential growth?

Back

Use the formula A = P(1 + r)^t, where A is the future value, P is the principal, r is the growth rate, and t is the time in years.

Front

How do you calculate the future value of an investment with exponential decay?

Back

Use the formula A = P(1 - r)^t, where A is the future value, P is the principal, r is the decay rate, and t is the time in years.

Front

What is the significance of the interest rate in exponential growth problems?

Back

The interest rate determines how quickly the investment grows; a higher rate results in more significant growth over time.

Front

What does it mean for a quantity to decrease by a percentage each year?

Back

It means that each year, the quantity is reduced by that percentage of its current value, leading to a smaller amount each subsequent year.

Front

How do you round numbers in exponential problems?

Back

Round to the nearest whole number or cent as specified in the problem, ensuring accuracy in financial calculations.

Front

What is the impact of compounding frequency on interest earned?

Back

More frequent compounding (e.g., monthly vs. annually) results in more interest earned over time due to interest being calculated on previously earned interest.

Front

How do you interpret a 10% annual decrease in subscribers?

Back

It means that each year, the number of subscribers is reduced to 90% of the previous year's total.