Exponential Growth and Decay

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 doubles every 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, radioactive substances decay exponentially over time.

The general 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.

The general 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.

The y-intercept of an exponential function is the value of the function when $$x = 0$$ . It represents the initial amount before any growth or decay occurs.

Exponential growth is identified on a graph by a curve that rises steeply to the right, indicating that the quantity increases rapidly over time.

Exponential decay is identified on a graph by a curve that falls steeply to the right, indicating that the quantity decreases rapidly over time.

The value is $$486$$ .

This sequence is an example of exponential growth.

This sequence is an example of exponential decay.