The numbers (in thousands) of organ transplants in the United States in the years 2001

Chapter 5, Problem 112

(choose chapter or problem)

Comparing Models The numbers y (in thousands) of organ transplants in the United States in the years 2001 through 2006 are shown in the table, with x = 1 corresponding to 2001. (Source: Organ Procurement and Transplantation Network)

(a) Use the regression capabilities of a graphing utility to find the following models for the data.

\(y_{1}=a x+b\)          \(y_{2}=a+b \ln x\)

\(y_{3}=a b^{x}\)        \(y_{4}=a x^{b}\)

(b) Use a graphing utility to plot the data and graph each of the models. Which model do you think best fits the data?

(c) Interpret the slope of the linear model in the context of the problem.

(d) Find the rate of change of each of the models for the year 2004. Which model is increasing at the greatest rate in 2004?

Text Transcription:

y_1 = ax + b

y_2 = a + b ln x

y_3 = ab^x

y_4 = ax^b