Question

In the exponential decay model, \(y=C(1-r)^{t},\) what is the decay factor?

Short answer

The decay factor is \(1 - r\).

Step-by-step solution

Understand the Components of the Model

The exponential decay model is given by an equation in the form \(y = C(1 - r)^t\). In this equation, \(y\) is the quantity of interest. It depends on time \(t\). The coefficient \(C\) is the initial amount or size, \(r\) is the decay rate, and the decay factor we are looking for happens to be \(1 - r\).

Identify the Decay Factor

In our model, the decay factor is the value in the equation that is raised to the power of \(t\), the time. Given our model, that is \(1 - r\). So, the decay factor for the provided exponential decay model is \(1 - r\).