In a block of fuel the multiplication factor is k = 1.01, and in another it is k = 1.10…

Step 1. The generations. $\dfrac{10\ \text{ms}}{0.1\ \text{ms}} = 100$ generations.

Step 2. The growth. For $k = 1.01$: $1.01^{100} = 2.70$. For $k = 1.10$: $1.10^{100} = 1.38 \times 10^{4}$.

Step 3. A tenfold rise. $1.10^g = 10$, so $g = \dfrac{\ln 10}{\ln 1.10} = \dfrac{2.303}{0.0953} = 24.2$ generations. That is only $2.4$ ms.

Why delayed neutrons matter. If every neutron came at once, even $k = 1.01$ would more than double the power in $10$ ms, too fast for any machine to follow. About $0.65\ \%$ of the neutrons come seconds late. The average time between generations then becomes about $0.1$ s, a thousand times longer, and for $k$ just above $1$ the power rises over seconds. The control rods have time to act.