Which description best defines Exponential Decay?

Which description best defines Exponential Decay?

• A. The total value decreases but the proportion that leaves remains constant over time.
• B. The growth rate accelerates over time.
• C. The size remains constant.
• D. The value increases at a decreasing rate.

Answer: (A)

Exponential decay means a quantity decreases at a rate proportional to how much is left. In equal time intervals, the same fraction of the current amount leaves, so the absolute amount removed in a step is large at first and gets smaller later, but the fraction that leaves each moment stays constant. That’s why the total value goes down while the proportion that leaves per unit time remains the same. A simple way to see this is N(t) = N0 e^{-kt} with k > 0, which implies dN/dt = -k N. The constant k is the constant fractional decay rate, exactly describing a steady percentage loss over time. The other descriptions describe growth, no change, or growth that tapers off rather than decay, so they don’t match exponential decay.

Exponential decay means a quantity decreases at a rate proportional to how much is left. In equal time intervals, the same fraction of the current amount leaves, so the absolute amount removed in a step is large at first and gets smaller later, but the fraction that leaves each moment stays constant. That’s why the total value goes down while the proportion that leaves per unit time remains the same.

A simple way to see this is N(t) = N0 e^{-kt} with k > 0, which implies dN/dt = -k N. The constant k is the constant fractional decay rate, exactly describing a steady percentage loss over time.

The other descriptions describe growth, no change, or growth that tapers off rather than decay, so they don’t match exponential decay.