Exponential Growth & Decay

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, leading to rapid increases as time progresses.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time, leading to rapid decreases as time progresses.

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

How do you calculate the growth factor?

Back

The growth factor is calculated as 1 + r, where r is the growth rate expressed as a decimal.

Front

How do you calculate the decay factor?

Back

The decay factor is calculated as 1 - r, where r is the decay rate expressed as a decimal.

Front

If a quantity increases by 60% each year, what is the growth factor?

Back

The growth factor is 1.6.

Front

If a quantity decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.8.

Front

What does the graph of Exponential Growth look like?

Back

The graph of Exponential Growth rises steeply and curves upwards as time increases.

Front

What does the graph of Exponential Decay look like?

Back

The graph of Exponential Decay falls steeply and approaches zero as time increases.