A sample of 80 bacteria grows exponentially and increases by 47% each hour.

  1. How many bacteria will there be after 18 hours?
  2. How long does it take for the population to double?

  1. Using LaTeX: \displaystyle P=P_0e^{kt} gives LaTeX: \displaystyle P=80e^\frac{47 t}{100} . Evaluating at LaTeX: \displaystyle t=18 gives LaTeX: \displaystyle P=377765 bacteria.
  2. The doubling time is LaTeX: \displaystyle t=\frac{\ln 2}{k}=1.47 hours