1. Advanced Precalculus Notes 4.9 Building Exponential, Logarithmic, and Logistic Models

2. Exponential Model Year (x) Price (y) 1986 t=0 1987 t=1.392 1988 t=2.7652 1989 t=31.1835 1990 t=41.1609 1991 t=52.6988 1992 t=64.5381 1993 t=75.3379 1994 t=86.8032 Year (x) Price (y) 1995 t=97.0328 1996 t=1011.5585 1997 t=1113.4799 1998 t=1223.5424 1999 t=1331.9342 2000 t=1439.7277 2001 t=1554.31 2002 t=1646.20 2003 t=1747.53 The above data represents the closing price of Harley Davidson stock at the end of each year. a) Using a scatter plot, graph the data.

4. b) Use the regression capabilities of the calculator to fit an exponential function to the data. c) Express the equation in the form d) Graph the equation in (c) and use it to predict the price of the stock in 2004. 2010 actual price: $31.62 e) What does k represent in the equation?

5. Logarithmic Model Pressure (p) mm. Mercury 760740725700650630600580550 Height (h) kilometers 0.184.328.5651.0791.2911.6341.8622.235 That above data represents the relation between the height of a weather balloon. a) Using a scatter plot, graph the data. b) Use the regression capabilities of the calculator to fit a logarithmic function to the data. c) Express the equation in the form d) Graph the equation in (c) and use it to predict the height of the balloon if the atmospheric pressure is 560 mm.

7. Logistic Model Time Hours Yeast Biomass 09.6 118.3 229.0 347.2 471.1 5119.1 6174.6 7257.3 8350.7 Time Hours Yeast Biomass 9441.0 10513.3 11559.7 12594.8 13629.4 14640.8 15651.1 16655.9 17659.6 18661.8

8. The given data represents the amount of yeast biomass in a culture after t hours. a) Using a scatter plot, graph the data. b) Use the regression capabilities of the calculator to fit a logistic function to the data. c) Express the equation in the form d) Graph the equation in (c) and use it to predict the population of the culture at t = 19 hours.

10. Assignment: page 342: 1, 7, 9