SOLUTION: The doubling time for e-coli= 20 minutes Mass of the e-coli bacterium =10 to the -12g Mass of the earth =5.9763* 10 to the 24kg • What is the mass of a colony of e coli af

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Question 102611: The doubling time for e-coli= 20 minutes
Mass of the e-coli bacterium =10 to the -12g
Mass of the earth =5.9763* 10 to the 24kg


• What is the mass of a colony of e coli after 1 day (24hrs) of exponential growth from one single e-coli bacterium?

• How long would it take to reach a mass equivalent to planet earth?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Doubling time = 20 minutes
Mass of e. coli = 1x10%5E-12g
Mass of earth = 5.9763x10%5E24kg
For exponential growth problems, we need to determine the growth constant, k, which is related to the doubling time, T, by the following equation:
k=ln%282%29%2FT
k=ln%282%29%2F20
k=3.47x10%5E-2
The general form of an exponential equation is
1. Find m at t=24 hours=1440 minutes, since doubling time is given in minutes for consistency.
kt=%283.47x10%5E-2%29%281440%29
kt=49.968
m+=+m%5B0%5D%2Ae%5E%2849.906%29
m+=+1x10%5E-12%2Ae%5E%2849.906%29
m+=+1x10%5E-12%2A4.72237x10%5E21
m+=+4.72x10%5E9
Sice we're have mass and are looking for time, let's re-arrange the equation.
ln%28m%29-ln%28m%5B0%5D%29=kt
t=%28ln%28m%29-ln%28m%5B0%5D%29%29%2Fk
Note 1 kg = 1000 g, the mass of the earth was converted to grams to keep units consistent.
2. t=%28ln%285.9763x10%5E27%29-ln%281x10%5E-12%29%29%2F%283.47x10%5E-2%29
t=2639 minutes
Thank goodness for that anti-bacterial soap.