In the activity equation A = A0 e^{-λ t}, which parameters determine A?

In the activity equation A = A0 e^{-λ t}, which parameters determine A?

• A. A0, λ, t
• B. t and λ only
• C. A0 only
• D. λ and A0 only

Answer: (C)

The current activity is set by three things at once: the starting activity, how quickly it decays, and how long it has been decaying. The formula A = A0 e^{-λ t} shows A scales with the initial value A0 and is reduced by the exponential factor that depends on both the decay constant λ and the elapsed time t. Because the exponential term changes with either λ or t, both parameters influence A, not just one. If you only know A0, you won’t know A after some time without λ and t. If you know t and λ, you still need A0 to know the actual current activity. If you know A0 and λ, you still need t to know how far decay has progressed. Therefore, A is determined by A0, λ, and t.

The current activity is set by three things at once: the starting activity, how quickly it decays, and how long it has been decaying. The formula A = A0 e^{-λ t} shows A scales with the initial value A0 and is reduced by the exponential factor that depends on both the decay constant λ and the elapsed time t. Because the exponential term changes with either λ or t, both parameters influence A, not just one. If you only know A0, you won’t know A after some time without λ and t. If you know t and λ, you still need A0 to know the actual current activity. If you know A0 and λ, you still need t to know how far decay has progressed. Therefore, A is determined by A0, λ, and t.