A sample of 10000 bacteria grows exponentially and increases by 33% each hour.

  1. How many bacteria will there be after 8 hours?
  2. How long does it take for the population to double?

  1. Using LaTeX: \displaystyle P=P_0e^{kt} gives LaTeX: \displaystyle P=10000e^\frac{33 t}{100} . Evaluating at LaTeX: \displaystyle t=8 gives LaTeX: \displaystyle P=140132 bacteria.
  2. The doubling time is LaTeX: \displaystyle t=\frac{\ln 2}{k}=2.1 hours