Question

1. what does the t represent in the exponential decay formula $n = n_0 cdot (0.5)^{\frac{t}{t}}$?

a. the initial quantity

b. the decay constant

c. the rate of decay

d. the time elapsed

Explanation:

In the exponential decay formula \( N = N_0 \cdot (0.5)^{\frac{t}{T}} \) (assuming \( T \) is the half - life, though in the given formula the denominator of the exponent with \( t \) is not fully shown, but the general form of exponential decay related to half - life has time as a variable), \( N_0 \) is the initial quantity, the base of the exponential (here 0.5) is related to the decay factor, and \( t \) represents the time that has passed (elapsed) since the start of the decay process. Option a is wrong because \( N_0 \) is the initial quantity. Option b is wrong as the decay constant is a different parameter (usually denoted as \( \lambda \) in the \( N = N_0e^{-\lambda t} \) form). Option c is wrong as the rate of decay is related to how fast the quantity is decreasing, and \( t \) is not the rate. So \( t \) represents the time elapsed.

Answer:

d. The time elapsed