A population of bacteria is growing in such a way a that the number of bacteria present, N, after t minutes is given by the rule #N=42e^(0.0134t)#. How long will it be before the population bacteria doubles?

1 Answer
Mar 30, 2017

51.73 minutes.

Explanation:

  1. Let the population be #N# at #t=t_1#.
  2. Let the population be twice i.e. #2*N# at #t=t_2#.

#therefore delta t = t_2-t_1 # where #delta t# is the time required for population to double.

#therefore# we obtain two equations from above conditions:-

  1. #N = 42*e^(0.0134*t_1)#
  2. #2*N = 42*e^(0.0134*t_2)#

Dividing these equations

#2 = e^(0.0134*(t_2-t_1)) = e^(0.0134*delta t)#

Taking natural logarithm on both sides;
#ln(2) = 0.0134 * delta t#
#implies##delta t = 51.73#