\section*{Problem 2}

We can use the startup rate equation assuming \(\dot \lambda_{eff}, S = 0\) to
solve this problem:

\[SUR = 26.06 [dpm-sec] \frac{\dot \rho + \lambda_{eff} \rho}{\beta - \rho}\]

To get from \(10^{-6}\%\) to \(10^{1}\%\) power in 50 minutes, we can find that:

\[SUR = \frac{1-(-6)}{50} \frac{\text{decades}}{\text{minutes}} = 0.14
\text{DPM}\]

We then plug in our values (assume \(\dot \rho = 0\) with a step change):

\[0.14  = 26.06 [dpm-sec] \frac{0 + 0.1 \rho}{\beta - \rho}\]
\[0.14 \beta - 0.14 \rho= 2.606 \rho\]

\[\boxed{\rho = 0.0509\beta}\]

Thus the correct answer is C.