A bacterial culture starts with 706 bacteria and doubles in size every 8.0 hours. Write a model for the number of bacteria after $LaTeX: \displaystyle t$ hours.

Since the population dobules every 8.0 hours the function must contain the points $LaTeX: \displaystyle (0,706), (1, 1412)$ , and $LaTeX: \displaystyle (2,2824)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{t}{8}$ . The model is $LaTeX: \displaystyle P=706\cdot 2^\frac{t}{8}$ .