3 (MATH 4300-01) Due date: Friday, Oct. 2, 2015 1. Name (Print): Consider the following data. x y 0 1 2 3 4 30 10 13 20 25 Assume that the data set can be described by a function y = c + a x ebx, where a, b, and c are any constants. a) Linearize y = c + a x ebx and use the data to test the suitability of this assumption. Find a linear function for this data plot. b) Graph the table data and the model that follows from the above relation. c) Calculate the relative error of your model in %. d) Calculate the maximum of y(x). 2. The U.S. Bureau of Public Roads determined the following total stopping distances D (in ft) depending on the velocity v (in mph) of cars. v 20 30 40 50 60 70 80 D 42 73.5 116 173 248 343 464 a) Use the data to plot ln D versus v and ln v. Compare the data with linear functions that reveal the parameters of corresponding exponential and power function models. b) Use the data to plot D / v. Compare the data with a linear and a quadratic function. c) Plot D according to the original data in comparison to the two models for D / v. Calculate the relative error of the two polynomial models. d) Discuss the suitability of the models obtained for D. Identify one model that provides a formula that can be used to calculate the total stopping distance without using a calculator. Illustrate the use of this formula by three examples