What process describes a decrease that occurs at a rate proportional to the current value?

The process described is known as exponential decay, which occurs when a quantity decreases at a rate that is proportional to its current value. In mathematical terms, this can be expressed with the differential equation ( \frac{dy}{dt} = -ky ), where ( y ) represents the quantity in question, ( t ) is time, and ( k ) is a positive constant that signifies the rate of decay. This means that the larger the quantity is, the faster it declines, leading to a process that is characterized by rapid decreases initially, which slow down over time.

This nature of exponential decay results in a distinctive curve when graphed, showing a rapid decline at first that gradually flattens out. Understanding exponential decay is crucial in fields such as physics, biology, and finance, where processes like radioactive decay, population decline, and depreciation of assets can be modeled with this principle.

Linear decay, on the other hand, describes a constant rate of decrease, which does not depend on the current value. Quadratic decay involves a decrease that changes over time based on the square of the variable, while logarithmic decay represents a much slower decrease but also does not relate directly to the current value in proportionate terms.

In summary,