A sample of 1600 bacteria grows exponentially and increases by 49% each hour.

  1. How many bacteria will there be after 35 hours?
  2. How long does it take for the population to double?

  1. Using LaTeX: \displaystyle P=P_0e^{kt} gives LaTeX: \displaystyle P=1600e^\frac{49 t}{100} . Evaluating at LaTeX: \displaystyle t=35 gives LaTeX: \displaystyle P=44902481985 bacteria.
  2. The doubling time is LaTeX: \displaystyle t=\frac{\ln 2}{k}=1.41 hours