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 decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

What does the initial value represent in an exponential function?

Back

The initial value is the starting amount before any growth or decay occurs, often represented as 'a' in the function y = a(b)^x.

Front

In the function y = 5000(0.98)^x, what does 0.98 represent?

Back

0.98 represents the decay factor, indicating that the amount decreases by 2% each year.

Front

How do you convert a percentage decrease to a decay factor?

Back

To convert a percentage decrease to a decay factor, subtract the percentage (as a decimal) from 1. For example, a 14.9% decrease becomes 1 - 0.149 = 0.851.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(x) = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

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

Back

In exponential functions, 'x' usually represents time, often measured in years, months, or other time intervals.

Front

How can you identify an exponential growth situation from a graph?

Back

An exponential growth graph will show a curve that rises steeply, indicating that the quantity increases rapidly over time.

Front

How can you identify an exponential decay situation from a graph?

Back

An exponential decay graph will show a curve that falls steeply at first and then levels off, indicating that the quantity decreases rapidly at first and then slows down.