A bacterial culture starts with 175 bacteria and doubles in size every 1.5 hours. Write a model for the number of bacteria after $LaTeX: \displaystyle t$ hours.

Since the population dobules every 1.5 hours the function must contain the points $LaTeX: \displaystyle (0,175), (1, 350)$ , and $LaTeX: \displaystyle (2,700)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{2 t}{3}$ . The model is $LaTeX: \displaystyle P=175\cdot 2^\frac{2 t}{3}$ .