Final answer:
C. The exponential decay model is Q = 1,900e^(-0.693t), where 1,900 is the initial amount and 0.693 is the decay constant associated with a half-life of 1.
Step-by-step explanation:
The correct answer is option C. 1,900e^(-0.693t). When addressing exponential decay, an initial quantity Q decreases over time t according to the formula Q = Q0e(−kt), where Q0 is the initial amount, e is the base of the natural logarithm, and k is the decay constant.
In this scenario, the half-life of the substance is given as 1, which means after time t = 1, the quantity Q will be half of its original value, Q0. The decay constant k for a half-life of 1 can be calculated using k = (ln 2) / t1/2 = 0.693. Since the initial amount Q0 is 1,900, the equation representing the exponential decay is Q = 1,900e(−0.693t).
The correct answer is option C. The exponential decay or growth model for the given data can be represented by the equation Q = 1,900e^(-0.693t), where Q is the quantity at time t.
In this equation, the coefficient -0.693 represents the decay constant, which is related to the half-life of the decay. To find the associated decay model, we use the given half-life of 1 and substitute it into the equation.
Substituting t = 1 into the equation, we get Q = 1,900e^(-0.693 * 1) = 1,900e^(-0.693) ≈ 950.
Therefore, the correct exponential decay model for the given data is Q = 950e^(-0.693t).