Suppose that a single bacterium exists at 11:00am. It divides into two bacteria at 11:01, and the population continues to double every minute. If each bacterium has a volume of 10^-21m^3, approximately how deep would the bacteria be at 1:09pm if they were spread in a uniform layer all over the surface of the Earth? (Assume that the surface area of the Earth is 5.1*10^14m^2, and show your work.)
a) 468 m b) 1334 m c)589 m d) 1024 m

Question

Suppose that a single bacterium exists at 11:00am. It divides into two bacteria at 11:01, and the population continues to double every minute. If each bacterium has a volume of 10^-21m^3, approximately how deep would the bacteria be at 1:09pm if they were spread in a uniform layer all over the surface of the Earth? (Assume that the surface area of the Earth is 5.1*10^14m^2, and show your work.)
a) 468 m  b) 1334 m  c)589 m  d) 1024 m

kropot72 · Answer

Number of bateria = 2^n where n is the number of minutes between 11:00am and 1:09pm
$$Number\ of\ bacteria=2^{129}$$
$$Total\ volume\ of\ bacteria=2^{129}\times 10^{-21}\ m ^{3}$$
Depth of bacteria = (total volume of bacteria)/(surface area of the earth)