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 accelerating 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 linear growth?

Back

Linear growth occurs when a quantity increases by a constant amount over equal intervals of time, resulting in a straight line when graphed.

Front

What is linear decay?

Back

Linear decay occurs when a quantity decreases by a constant amount over equal intervals of time, resulting in a straight line with a negative slope when graphed.

Front

How can you identify exponential growth on a graph?

Back

Exponential growth is identified by a curve that rises steeply and becomes increasingly steep 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 and becomes less steep as it moves to the right.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What is the difference between exponential and linear growth?

Back

Exponential growth increases at an accelerating rate, while linear growth increases at a constant rate.

Front

What is the difference between exponential and linear decay?

Back

Exponential decay decreases at a decreasing rate, while linear decay decreases at a constant rate.