A sample of 6000 bacteria grows exponentially and increases by 4% each hour.

  1. How many bacteria will there be after 24 hours?
  2. How long does it take for the population to double?

  1. Using LaTeX: \displaystyle P=P_0e^{kt} gives LaTeX: \displaystyle P=6000e^\frac{t}{25} . Evaluating at LaTeX: \displaystyle t=24 gives LaTeX: \displaystyle P=15670 bacteria.
  2. The doubling time is LaTeX: \displaystyle t=\frac{\ln 2}{k}=17.33 hours