Problem
It takes 21 minutes for a certain population of bacteria to double. If there are \( 8,014,627 \) bacteria in this population at 10 a.m., what is the best estimate, in millions, of the number of bacteria at 10:42 a.m. on the same day?
Solution
Step 1 ：\( T = 42 \textrm{ min} \)
Step 2 ：\( n = \frac{T}{21} = \frac{42}{21} = 2 \)
Step 3 ：\( B = 8014627 \times 2^n = 8014627 \times 2^2 = 8014627 \times 4 = 32058508 \)
Step 4 ：\( \textrm{Estimate in millions} = \frac{B}{10^6} = \frac{32058508}{10^6} \approx 32.06 \)
