Which of the following statements is the best description of exponential decay?

A.
Exponential behavior occurs when a function increases at a rate of increasing value.
B.
Exponential behavior occurs when a function increases at a rate of decreasing value.
C.
Exponential behavior occurs when a function increases or decreases at a rate proportional to its current value.
D.
Exponential behavior occurs when a function increases or decreases at a rate proportional to its initial value.

Is D correct?

C is correct

No, D is not the correct statement. The best description of exponential decay is option B: "Exponential behavior occurs when a function increases at a rate of decreasing value." In exponential decay, a function starts at a certain value and decreases over time at a decreasing rate.

No, option D is not the correct description of exponential decay. The correct answer is B.

To understand why option B is the best description of exponential decay, let's break down the concept. Exponential decay refers to a process where a quantity decreases at a constant percentage or rate over time.

In option A, it says that exponential behavior occurs when a function increases at a rate of increasing value, which is opposite to the definition of exponential decay.

Option C states that exponential behavior occurs when a function increases or decreases at a rate proportional to its current value. While this definition fits exponential growth, it does not specifically describe exponential decay.

That leaves us with option B, which accurately describes exponential decay. It states that exponential behavior occurs when a function increases at a rate of decreasing value. In other words, as time passes, the decrease in quantity gets smaller and smaller relative to the original value.

So, in conclusion, option B is the best description of exponential decay.