Exponential Growth vs. Decay Flashcard

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. For example, if a population grows by 5% each year, it is experiencing exponential growth.

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. For example, if a radioactive substance decays by 10% each year, it is experiencing exponential decay.

The general form of an exponential growth function is $$y = a \times b^x$$ , where $$a > 0$$ and $$b > 1$$ .

The general form of an exponential decay function is $$y = a \times b^x$$ , where $$a > 0$$ and $$0 < b < 1$$ .

In an exponential function, the base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor. It determines how quickly the function increases or decreases.

If the base of the exponent is greater than 1, the function represents exponential growth. If the base is between 0 and 1, it represents exponential decay.

The initial value 'a' in an exponential function represents the starting amount or quantity at $$x = 0$$ .

The graph of an exponential growth function rises steeply as x increases, showing a rapid increase in value.

The graph of an exponential decay function falls steeply as x increases, showing a rapid decrease in value.

An example of exponential growth is the increase in a population of bacteria that doubles every hour.