Which of the following best describes the complementary function for I-135 in the decay equation?

The complementary function for I-135 in the decay equation is described by the exponential decay form, represented as A exp(-λ_i t). This expression captures the essence of radioactive decay, which is characterized by a continuous and exponential decrease in the quantity of the radioactive isotope over time.

In this context, "A" is a constant that represents the initial quantity of I-135 at time t = 0, and "λ_i" is the decay constant specific to I-135, indicating the rate at which the isotope decays. The term "t" denotes time, and the negative exponent reflects that as time increases, the value of exp(-λ_i t) diminishes, showing the reduction in the quantity of I-135.

Other forms in the options are not suitable for describing the complementary function in radioactive decay. For instance, the sine and cosine functions typically represent oscillatory behavior, which does not align with the nature of radioactive decay that is always decreasing over time. The expression that includes a sum of a constant and an exponential term does not accurately represent the behavior of a purely decaying system either, as it suggests an asymptotic approach towards a non-zero value, which contradicts the expected behavior of a substance like I-135