1. A physicist, a biologist, and a mathematician are sitting on a bench across from a house. They watch as two people go into the house, and then a little later, three people walk out. The physicist says, "The initial measurement was incorrect." The biologist says, "They must have reproduced." And the mathematician says, "If exactly one person enters that house, it will be empty."

2. 2.5: Exponential Models FST

3. Exponential Models In an experiment on the population growth of insects, there were 74 insects three days after the beginning of the experiment and 108 insects after an additional two days. 1.Make a table of these data 2.a. Find a linear model for the data b. Find an exponential model for the data c. Which model makes more sense? 3. Graph the function 4.Find the initial number of insects 5.Predict the number of insects 6.5 days after the beginning of the experiment

4. Breaking Strength Diameter (mm) 581214162230364048 Breaking Strength (lb) 37804590 The table below contains breaking strength data for new 3- strand polypropylene fiber rope. 1.Use the data points (12, 3780) and (14, 4590) and a system of equations to determine an exponential model for the data.

5. Breaking Strength Diameter (mm) 581214162230364048 Breaking Strength (lb) 78017103780459055801035019350273503195046800 The table below contains breaking strength data for new 3- strand polypropylene fiber rope. 1.Use the data points (12, 3780) and (14, 4590) and a system of equations to determine an exponential model for the data. 2.Use the entire data set to find an exponential model to match the data. 3.Which model better represents the data? Defend your answer. 4.Use the equation to estimate the breaking strength of 44mm diameter rope.

6. Exponential Models In 2005, Erin purchased a $50 U.S. Savings Bond for $25. Assume the bond has a constant annual yield of 0.5%. (Note: The annual yield on bonds is not always constant. $50 is the amount the bond is worth when it reaches maturity.) a)Express the value of the bond as a function of n, the number of years after 2005. b)Use a calculator and the equation found in (a) to estimate the doubling time for the value of the bond.

7. Exponential Models

8. Homework pp 116 – 117: 1-5, 7, 8, 9, 10, 13