A student investigates the kinetics of the reaction represented by the equation below.

\[ \text{A}\text{(aq)} + 2\,\text{B}\text{(aq)} \rightarrow \text{C}\text{(aq)} \]

To determine the rate law, the student performs three trials at \(298\text{ K}\) in which \(\text{B}\text{(aq)}\) is present in large excess (\([\text{B}]_0 \gg [\text{A}]_0\)), so that \([\text{B}]\) remains essentially constant throughout each trial. Under these conditions, the rate law is given by:

\[ \text{Rate} = k'[\text{A}]^m \]

where \(k' = k[\text{B}]_0^n\). In each trial, a plot of \(\ln[\text{A}]\) versus time yields a straight line. The experimental data collected are shown in the following table.

Trial	\([\text{A}]_0\text{ (M)}\)	\([\text{B}]_0\text{ (M)}\)	\(k'\text{ (s}^{-1}\text{)}\)
1	\(1.0 \times 10^{-4}\)	\(0.10\)	\(2.0 \times 10^{-3}\)
2	\(2.0 \times 10^{-4}\)	\(0.10\)	\(2.0 \times 10^{-3}\)
3	\(1.0 \times 10^{-4}\)	\(0.20\)	\(8.0 \times 10^{-3}\)

Which of the following is the rate law for the reaction and the calculated value of the rate constant, \(k\)?