Exponential Growth and Decay

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 process by which a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Front

What is the decay factor in exponential decay?

Back

The decay factor is calculated as 1 minus the decay rate (expressed as a decimal). For example, if the decay rate is 8%, the decay factor is 0.92.

Front

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

Back

The future value can be calculated using the formula: FV = P(1 + r)^t, where P is the initial amount, 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

The future value can be calculated using the formula: FV = P(1 - r)^t, where P is the initial amount, r is the decay rate, and t is the time in years.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = P(1 + r)^t, where y is the future value, P is the initial amount, r is the growth rate, and t is the time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = P(1 - r)^t, where y is the future value, P is the initial amount, r is the decay rate, and t is the time.

Front

What does the variable 'x' represent in exponential functions?

Back

In exponential functions, 'x' typically represents the time period (often in years) over which growth or decay occurs.

Front

How do you express a population decrease of 6% per year in an equation?

Back

You can express it as y = P(0.94)^t, where P is the initial population and 0.94 represents the remaining population after a 6% decrease.

Front

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

Back

The base in an exponential function indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.