A bacterial culture starts with 174 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 $LaTeX: \displaystyle (0,174), (1, 348)$ , and $LaTeX: \displaystyle (2,696)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{t}{6}$ . The model is $LaTeX: \displaystyle P=174\cdot 2^\frac{t}{6}$ .