A sample of 30 bacteria grows exponentially and increases by 46% each hour.

  1. How many bacteria will there be after 16 hours?
  2. How long does it take for the population to double?

  1. Using LaTeX: \displaystyle P=P_0e^{kt} gives LaTeX: \displaystyle P=30e^\frac{23 t}{50} . Evaluating at LaTeX: \displaystyle t=16 gives LaTeX: \displaystyle P=47155 bacteria.
  2. The doubling time is LaTeX: \displaystyle t=\frac{\ln 2}{k}=1.51 hours