Final answer:
To find the value of the constant k in the equation (dy)/(dt) = ky, additional specific information or initial conditions are necessary. Without such details, we cannot determine the numerical value for k.
Step-by-step explanation:
The student is asking for the value of the constant k in the exponential decay model, which is used to describe processes such as the decay of a substance over time. In the equation (dy)/(dt) = ky, where y is the quantity at time t and k is a constant, we recognize this as a first-order linear differential equation that models exponential growth or decay. If the student provided a specific initial condition or additional data, we could determine the exact value of k by solving the differential equation.
Without additional information such as initial conditions, we cannot provide a numerical value for the constant k. It is clearer in contexts such as radioactive decay, chemical reaction rates, or population growth where specific values can be measured or given in the problem statement.
Typically, to determine the value of k, we would need a set of data that shows how the quantity y changes over time or at least two points to form a ratio to solve for k.