Question 102611
Doubling time = 20 minutes

Mass of e. coli = {{{1x10^-12}}}g

Mass of earth = {{{5.9763x10^24}}}kg
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(2)/T}}}
{{{k=ln(2)/20}}}
{{{k=3.47x10^-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=(3.47x10^-2)(1440)}}}
{{{kt=49.968}}}
{{{m = m[0]*e^(49.906)}}}
{{{m = 1x10^-12*e^(49.906)}}}
{{{m = 1x10^-12*4.72237x10^21}}}
{{{m = 4.72x10^9}}}
Sice we're have mass and are looking for time, let's re-arrange the equation. 
{{{ln(m)-ln(m[0])=kt}}}
{{{t=(ln(m)-ln(m[0]))/k}}}
Note 1 kg = 1000 g, the mass of the earth was converted to grams to keep units consistent. 
2. {{{t=(ln(5.9763x10^27)-ln(1x10^-12))/(3.47x10^-2)}}}
t=2639 minutes
Thank goodness for that anti-bacterial soap.