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 accelerating rate. Example: Population growth where the number doubles over a fixed period.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, leading to a rapid decline. Example: Radioactive decay of a substance.

Front

What is the formula for exponential growth?

Back

The formula is: N(t) = N0 * e^(rt), where N(t) is the amount at time t, N0 is the initial amount, r is the growth rate, and e is Euler's number.

Front

What is the formula for exponential decay?

Back

The formula is: N(t) = N0 * e^(-rt), where N(t) is the amount at time t, N0 is the initial amount, r is the decay rate, and e is Euler's number.

Front

What does the term 'initial value' refer to in exponential functions?

Back

The initial value is the starting amount before any growth or decay occurs, often represented as N0 in the formulas.

Front

How can you identify exponential growth on a graph?

Back

Exponential growth is identified by a curve that rises steeply, showing that the rate of increase accelerates over time.

Front

How can you identify exponential decay on a graph?

Back

Exponential decay is identified by a curve that falls steeply, showing that the rate of decrease accelerates over time.

Front

What is a common characteristic of exponential functions?

Back

Exponential functions have a constant percentage rate of change, meaning they grow or decay by the same proportion over equal time intervals.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much larger values over time.

Front

What is a real-world example of exponential growth?

Back

A real-world example is the spread of a virus, where each infected person can infect multiple others, leading to rapid increases in cases.