A bacterial culture starts with 845 bacteria and doubles in size every 6.0 hours. Write a model for the number of bacteria after $LaTeX: \displaystyle t$ hours.

Since the population dobules every 6.0 hours the function must contain the points $LaTeX: \displaystyle (0,845), (1, 1690)$ , and $LaTeX: \displaystyle (2,3380)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{t}{6}$ . The model is $LaTeX: \displaystyle P=845\cdot 2^\frac{t}{6}$ .