Exponential Decay and Growth

Exponential Growth occurs when a quantity increases by a constant percentage over a period of time, resulting in a rapid increase. The general form of the equation is $$y = a(1 + r)^t$$ , where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Exponential Decay occurs when a quantity decreases by a constant percentage over a period of time, leading to a rapid decrease. The general form of the equation is $$y = a(1 - r)^t$$ , where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

The base of an exponential function indicates the growth or decay factor. For growth, the base is greater than 1 (e.g., 2, 3), and for decay, the base is between 0 and 1 (e.g., 0.5, 0.1).

Exponential Growth is identified by a curve that rises steeply as it moves from left to right, indicating that the quantity increases rapidly.

Exponential Decay is identified by a curve that falls steeply as it moves from left to right, indicating that the quantity decreases rapidly.

The growth rate is 90%, calculated as (1 - 0.10) * 100%.

The growth rate is 34%, calculated as (1.34 - 1) * 100%.

The growth rate is 80%, calculated as (1 - 0.2) * 100%.

The general form of an exponential decay equation is $$y = a(1 - r)^t$$ , where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.