A bacterial culture starts with 214 bacteria and doubles in size every 5.5 hours. Write a model for the number of bacteria after $LaTeX: \displaystyle t$ hours.

Since the population dobules every 5.5 hours the function must contain the points $LaTeX: \displaystyle (0,214), (1, 428)$ , and $LaTeX: \displaystyle (2,856)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{2 t}{11}$ . The model is $LaTeX: \displaystyle P=214\cdot 2^\frac{2 t}{11}$ .