Exponential Growth and Decay Concepts

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 is the process of reducing an amount by a consistent percentage rate over a period of time, leading to a decrease that slows down as the quantity decreases.

Front

What is the formula for calculating compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, 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

If a population of 21,517 grows by 11% annually, what is the formula to calculate the population after t years?

Back

Population = 21,517 * (1 + 0.11)^t.

Front

How do you calculate the value of an asset that depreciates by a fixed percentage each year?

Back

Value = Initial Value * (1 - depreciation rate)^number of years.

Front

What is the value of a $5,950 sailboat after 6 years if it depreciates by 11% per year?

Back

Value = 5,950 * (1 - 0.11)^6 = $2,957.04.

Front

What is the population of Bloom Falls after 3 years if it decreases by 4.5% annually?

Back

Population = 937 * (1 - 0.045)^3 = 816 people.

Front

What does it mean for a quantity to double in exponential growth?

Back

In exponential growth, a quantity doubles when it increases by 100% of its current value, which occurs at regular intervals depending on the growth rate.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount over time, while exponential growth increases by a percentage of the current value, leading to faster growth as the quantity increases.

Front

What is the significance of the base in an exponential function?

Back

The base of an exponential function determines the growth or decay rate; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.