Exponential Growth and Decay

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

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 is a Linear Function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you identify Exponential Growth on a graph?

Back

Exponential growth is identified by a curve that rises steeply, becoming steeper as it moves to the right.

Front

How can you identify Exponential Decay on a graph?

Back

Exponential decay is identified by a curve that falls steeply, becoming less steep as it moves to the right.

Front

What is the difference between Linear and Exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

If a quantity doubles every year, what type of growth is this?

Back

This is an example of Exponential Growth.

Front

If a quantity decreases by 20% each year, what type of decay is this?

Back

This is an example of Exponential Decay.