Step 1 :Given that the initial value of the toy tractor, \(V_0\), is $272 and the value of the toy tractor 11 years later, \(V(11)\), is $429, we can use the formula for exponential growth, \(V(t) = V_0 * e^{kt}\), to find the growth rate, \(k\).
Step 2 :Rearrange the formula to solve for \(k\): \(k = \frac{1}{t} * \ln(\frac{V(t)}{V_0})\).
Step 3 :Substitute the given values into the equation: \(k = \frac{1}{11} * \ln(\frac{429}{272})\).
Step 4 :Solving the equation gives \(k = 0.04142316842109269\).
Step 5 :Rounding to the nearest thousandth gives the final answer: \(\boxed{0.041}\).