A bacterial culture starts with 264 bacteria and doubles in size every 4.5 hours. Write a model for the number of bacteria after $LaTeX: \displaystyle t$ hours.

Since the population dobules every 4.5 hours the function must contain the points $LaTeX: \displaystyle (0,264), (1, 528)$ , and $LaTeX: \displaystyle (2,1056)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{2 t}{9}$ . The model is $LaTeX: \displaystyle P=264\cdot 2^\frac{2 t}{9}$ .