A bacterial culture starts with 541 bacteria and doubles in size every 6.5 hours. Write a model for the number of bacteria after $LaTeX: \displaystyle t$ hours.

Since the population dobules every 6.5 hours the function must contain the points $LaTeX: \displaystyle (0,541), (1, 1082)$ , and $LaTeX: \displaystyle (2,2164)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{2 t}{13}$ . The model is $LaTeX: \displaystyle P=541\cdot 2^\frac{2 t}{13}$ .