A bacterial culture starts with 761 bacteria and doubles in size every 7.0 hours. Write a model for the number of bacteria after $LaTeX: \displaystyle t$ hours.

Since the population dobules every 7.0 hours the function must contain the points $LaTeX: \displaystyle (0,761), (1, 1522)$ , and $LaTeX: \displaystyle (2,3044)$ . This gives a factor of $LaTeX: \displaystyle 2^\frac{t}{7}$ . The model is $LaTeX: \displaystyle P=761\cdot 2^\frac{t}{7}$ .