Suppose a value is decaying, and 44$\%$ remains after $1000$ years. The amount of the substance can be modeled by the function $$f(t) = Ae^{kt}$$ where $A$ is the initial amount, $t$ is the number of years, and the constant $k$ is the continuous rate of decay. Find the value of $k\text{.}$ Answer: $k =$