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)N=42e0.0134t. How long will it be before the population bacteria doubles?

1 Answer
Mar 30, 2017

51.73 minutes.

Explanation:

  1. Let the population be NN at t=t_1t=t1.
  2. Let the population be twice i.e. 2*N2N at t=t_2t=t2.

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
impliesdelta t = 51.73