The value of a car depreciates according to the formula \(V(t) = V_0 e^{-kt}\), where \(V_0\) is the initial value of the car, \(V(t)\) is the value of the car after \(t\) years, and \(k\) is the depreciation constant. Suppose a car was initially valued at $20,000 and after 3 years, its value is $12,000. Find the depreciation constant \(k\). Let's think step by step and output the final answer within \boxed{}.
user