A bacterial culture starts with 560 bacteria and doubles in size every 8.5 hours. Write a model for the number of bacteria after $LaTeX: \displaystyle t$ hours.

Since the population dobules every 8.5 hours the function must contain the points $LaTeX: \displaystyle (0,560), (1, 1120)$ , and $LaTeX: \displaystyle (2,2240)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{2 t}{17}$ . The model is $LaTeX: \displaystyle P=560\cdot 2^\frac{2 t}{17}$ .