A sample of 90 bacteria grows exponentially and increases by 6% each hour.

  1. How many bacteria will there be after 12 hours?
  2. How long does it take for the population to double?

  1. Using LaTeX: \displaystyle P=P_0e^{kt} gives LaTeX: \displaystyle P=90e^\frac{3 t}{50} . Evaluating at LaTeX: \displaystyle t=12 gives LaTeX: \displaystyle P=185 bacteria.
  2. The doubling time is LaTeX: \displaystyle t=\frac{\ln 2}{k}=11.55 hours