Sanjay steps a logistic population with r = 0.8 per hour, K = 300 cells and N₀ = 5 cells, for 12…

Step 1. The wrong answer. $305.69$ cells is above $K = 300$ cells, which a logistic population never passes. The step of $2$ h is larger than $\dfrac{1}{r} = 1.25$ h, so each step jumps too far and overshoots.

Step 2. Exact. $N = \dfrac{300}{1 + 59 e^{-9.6}} = \dfrac{300}{1.00400} = 298.81$ cells.

Step 3. The small step. With $0.01$ h the stepped count agrees with the exact one to two decimal places.