Precalculus Name Lesson 3.6 - Nonlinear Models Exercise 1 Period Practice Regression. Use a calculator to create a scatter plot for the data given and determine which of the five models learned in class will best fit the data. Then use the regression tool on your calculator to find an equation for the function that models this data. Exercise 1. The data below shows the yield (in milligrams) of a chemical reaction over time (in minutes). Time (min) 1 2 3 4 15 6 7 8 Yield (mg) 1.5 7.4 10.2 13.4 15.8 16.3 18.2 18.3 a. What type of model best fits this data? b. Find an equation for the function that best models this data. Round all constants to the nearest thousandth. c. What are the practical domain and practical range of this model? Practical domain: Practical range: d. Use your model to find the following (round all answers to the nearest tenth). Then circle whether the evaluation is an example interpolation or extrapolation. 1) Find the yield after 90 seconds. interpolation extrapolation 2) Find the yield after 10 minutes. interpolation extrapolation e. How long will it take to obtain a yield of 25 mg? Solve algebraically. Exercise 2. The data shows the biomass (in grams per square meter) of a yeast culture over time (in hours). Time (h) 0 2 4 6 8 10 12 14 16 18 Biomass (g/m) 9.6 29.0 71.1 174.6 350.7 513.3 594.8 640.8 655.9 661.8 a. What type of model best fits this data? b. Find an equation for the function that best models this data. Round all constants to the nearest thousandth.c. What are the practical domain and practical range of this model? Practical range: Practical domain: d. Use your model to find the following (round all answers to the nearest tenth). Then circle whether the evaluation is an example interpolation or extrapolation. 1) Find the biomass after 5 hours. interpolation extrapolation 2) Find the biomass after 20 hours. interpolation extrapolation e. How long will it take to reach a biomass of 100? Solve algebraically. Exercise 3. The data shows the breaking point (in tons) of a steel cable with the given diameter (in inches). Diameter (in) 0.50 0.75 1.00 1.25 1.50 1.75 Breaking Point (tons) 9.85 21.80 38.30 59.20 84.40 114.00 a. What type of model best fits this data? b. Find an equation for the function that best models this data. Round all constants to the nearest thousandth. c. What are the practical domain and practical range of this model? Practical domain: Practical range: d. Use your model to find the following (round all answers to the nearest hundredth). Then circle whether the evaluation is an example interpolation or extrapolation. 1) Find the breaking point for a cable with a diameter of 0.25 in. interpolation extrapolation 2) Find the breaking point for a cable with a diameter of 7/8 in. interpolation extrapolatione. What must the diameter of a cable be to reach a breaking point of 200 tons? Solve algebraically. Exercise 4. The data shows the temperature (in F) of a cup of soup as it cools over time (in minutes) Time (min) 0 2 4 6 8 10 Temperature (OF) 180.2 165.8 146.3 135.4 127.7 110.5 a. What type of model best fits this data? b. Find an equation for the function that best models this data. Round all constants to the nearest thousandth. c. What are the practical domain and practical range of this model? Practical domain: Practical range: d. Use your model to find the following (round all answers to the nearest hundredth). Then circle whether the evaluation is an example interpolation or extrapolation. 1) Find the temperature of the soup after 30 seconds. interpolation extrapolation 2) Find the temperature of the soup after 15 minutes. interpolation extrapolation e. How long will it take the soup to cool to room temperature of 70 F? Solve algebraically. f. Rewrite your model as an exponential function in base e. Solve algebraically.Gaussian Models. Recall that Gaussian models are of the form f ( x ) = ae -(*-b) 2/ c This model is used in probability and statistics to represent populations with Normal distributions. The model for a Normal distribution with mean / and standard deviation o is written f ( x) = - =e-(x-1) 2/202 Exercise 5. On a recent SAT, the math scores for college-bound seniors roughly followed the normal distribution given by the equation D = 0.00356e -(x-511)2/25,088 200