at 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. at 10:15 a.m., there are 8 cells in the…

at 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. at 10:15 a.m., there are 8 cells in the bottle. at what time will there be 16 cells in the bottle? at what time will there be 64 cells in the bottle?

at 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. at 10:15 a.m., there are 8 cells in the bottle. at what time will there be 16 cells in the bottle? at what time will there be 64 cells in the bottle?

Answer

Answer:

  1. 10:20 a.m.
  2. 10:30 a.m.

Explanation:

Step1: Find the time - interval and growth pattern

From 10:05 a.m. to 10:15 a.m. (10 - minute interval), the number of bacteria grows from 2 to 8 (a factor of 4). So the bacteria double every 5 minutes.

Step2: Calculate time for 16 cells

Since 8 cells are at 10:15 a.m. and the bacteria double every 5 minutes, to get from 8 to 16 cells (a doubling), we add 5 minutes. So 16 cells will be at 10:20 a.m.

Step3: Calculate time for 64 cells

From 16 cells, to get to 64 cells, we note that $64\div16 = 4$, which means two more doublings. Each doubling takes 5 minutes, so we add $2\times5=10$ minutes to 10:20 a.m. So 64 cells will be at 10:30 a.m.