A sample of 20000 bacteria grows exponentially and increases by 40% each hour.

  1. How many bacteria will there be after 39 hours?
  2. How long does it take for the population to double?

  1. Using LaTeX: \displaystyle P=P_0e^{kt} gives LaTeX: \displaystyle P=20000e^\frac{2 t}{5} . Evaluating at LaTeX: \displaystyle t=39 gives LaTeX: \displaystyle P=119130760264 bacteria.
  2. The doubling time is LaTeX: \displaystyle t=\frac{\ln 2}{k}=1.73 hours