A culture starts with 400 cells and doubles every 25 minutes.

Step 1. The loop. $400 \times 2^{11} = 819\,200$ is still below a million, and $400 \times 2^{12} = 1\,638\,400$ is above. Twelve doublings take $12 \times 25 = 300$ min.

Step 2. The formula. $2^{t/25} = 2500$, so $t = 25 \times \log_2 2500 = 25 \times 11.29 = 282.2$ min.

Step 3. Why they differ. The loop checks the count only at the end of each doubling. The culture really passes a million part way through the twelfth doubling.