Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase. For example, if a population grows by 10% each year, it will grow faster each subsequent year.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease. For example, if a substance loses 20% of its mass every hour, it will decay faster each hour.

Front

Write the general formula for exponential growth.

Back

Front

Write the general formula for exponential decay.

Back

Front

Back

In the exponential function, the base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor. It indicates how much the quantity changes for each unit increase in x.

Front

If a population of bacteria doubles every hour, what type of growth is this?

Back

This is an example of exponential growth.

Front

If a car's value decreases by 15% each year, what type of function models this situation?

Back

This situation is modeled by an exponential decay function.

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is y = 0, meaning the value approaches zero but never actually reaches it.

Front

Back

The value 24000 represents the initial value of the car when t = 0.

Front

What does it mean if a function is described as having exponential decay?

Back

It means that the function's output decreases over time, typically represented by a base less than 1 in the exponential function.