How long does it take the culture to double its mass if a bacterial culture which is growing exponentially increases from 5 g to 7 g in 11 hours?

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Answer 1 · 2015-02-22T12:36:11

This is an example of a exponential function.

The form is always #N=B*g^t#
Where
#N#=new situation
#B#=begin
#g#=growth factor
#t#=time units

Now we fill in what we know:
#N=B*g^t->7=5*g^11->g^11=7//5=1.4#
Now grow factor #g# is the 11th root of #1.4#

You can do this on your calculator by #"1.4^(1/11)"# or
#1.4^(1/11)=1.03106...#

The growth factor can then be used in the equation:
#N=B*g^t->10=5*1.03106...^t->1.03106...^t=2#

From here on there are two ways to go:

(1) put this equation in your GC as Y1= and intersect with Y2=2

(2) Use logarithms:

#1.03106...^t=2->log 1.03106...^t=log2->#
#t*log1.03106...=log2->t=log2/log1.03106~~22.3#

Answer : a bit more than 22 hours. This is the doubling time from any start situation.