Solution
= Solution
The precursor exponential from part (e) has inverse period $\rho\lambda/(\beta-\rho)$. Hence
$$
\boxed{T_{\rm prompt\ jump}=\frac{\beta-\rho}{\rho\lambda}=60.0\ \mathrm s.}
$$
This is approximately $0.96\%$ shorter than the exact dominant period, so it slightly overestimates growth for these stipulated constants. Neglecting the small $\Lambda$ contribution is more accurate here than replacing the complete frequency dependence by its tangent at the origin.