Final answer:
The model equation for the decay of Strontium-89, a radioactive substance with a half-life of 50.5 days, is A = A₀e^(k*t), where A is the activity at time t, A₀ is the initial activity, k is the decay constant, and e is the base of the natural logarithm.
Step-by-step explanation:
The model equation for the decay of a radioactive substance with a half-life of 50.5 days is given by A = A₀e^(k*t), where A is the activity of the substance at time t, A₀ is the initial activity, k is the decay constant, and e is the base of the natural logarithm.
For Strontium-89, we can substitute the given values into the equation. Let's assume the initial activity A₀ is 100 (any arbitrary value). We can then solve for k using the half-life equation:
50.5 = (0.693/k)
k ≈ 0.01369 (rounded to five decimal places)
Substituting this value of k back into the model equation, we have A = A₀e^(0.01369t). This equation represents the decay of Strontium-89 over time.