12.17 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 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 number of years.

Front

What does it mean for a value to depreciate?

Back

Depreciation refers to the reduction in the value of an asset over time, often due to wear and tear or obsolescence.

Front

What is the significance of rounding in calculations?

Back

Rounding is used to simplify numbers to make them easier to work with, but it can also affect the accuracy of the final result.

Front

How does a percentage decrease affect a quantity?

Back

A percentage decrease reduces the quantity by that percentage of its current value, leading to a smaller final amount.

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has already been added.

Front

What is the impact of a higher interest rate on savings?

Back

A higher interest rate increases the amount of interest earned on savings, leading to a greater future value.