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. The general formula is $$A = a(1 + r)^t$$ , where A is the amount after time t, a is the initial amount, r is the growth rate, and t is time.

Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. The general formula is $$A = a(1 - r)^t$$ , where A is the amount after time t, a is the initial amount, r is the decay rate, and t is time.

Linear Growth increases by a constant amount over time, while Exponential Growth increases by a constant percentage, leading to much larger values over the same period.

The formula for Exponential Growth is $$A = a(1 + r)^t$$ .

The formula for Exponential Decay is $$A = a(1 - r)^t$$ .

In a graph, Exponential Growth appears as a curve that rises steeply, becoming steeper over time, while Linear Growth appears as a straight line.

In a graph, Exponential Decay appears as a curve that falls steeply, becoming less steep over time, while Linear Decay appears as a straight line.

In the exponential formulas, 'a' represents the initial amount or value before growth or decay occurs.

In the exponential formulas, 'r' represents the growth or decay rate expressed as a decimal.

In the exponential formulas, 't' represents the time period over which growth or decay occurs.