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 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 Exponential Growth?

Back

The formula is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for Exponential Decay?

Back

The formula is A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

What does the decay factor represent?

Back

The decay factor is the multiplier used in exponential decay, calculated as (1 - decay rate). For example, if the decay rate is 8%, the decay factor is 0.92.

Front

How do you calculate the population after a certain number of years with decay?

Back

Use the formula A = P(1 - r)^t, where P is the initial population, r is the decay rate, and t is the number of years.

Front

What is the difference between growth and decay in exponential functions?

Back

Growth increases the quantity over time, while decay decreases it. Growth uses (1 + r) and decay uses (1 - r) in their formulas.

Front

If a population of 10,000 decreases by 5% per year, what is the population after 1 year?

Back

Population after 1 year = 10,000(1 - 0.05) = 9,500.

Front

What is the significance of the base in exponential functions?

Back

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

Front

How do you identify if a model represents growth or decay?

Back

If the equation has a factor greater than 1, it represents growth; if it has a factor less than 1, it represents decay.