1. The problem involves three linear models representing sales from prescription drugs, hospital care revenue, and employment in the motion picture and sound recording industries. 2. For prescription drug sales, the model is $$y = 13.601x + 133.6$$ where $x=1$ corresponds to 2001. 3. a) To find sales in 2005, calculate $x = 2005 - 2000 = 5$ (since $x=1$ is 2001, $x=5$ is 2005). Then, $$y = 13.601 \times 5 + 133.6 = 68.005 + 133.6 = 201.605$$ billion. b) For 2010, $x = 2010 - 2000 = 10$, $$y = 13.601 \times 10 + 133.6 = 136.01 + 133.6 = 269.61$$ billion. 4. To find the year when sales reach 340 billion, solve for $x$: $$340 = 13.601x + 133.6$$ $$13.601x = 340 - 133.6 = 206.4$$ $$x = \frac{206.4}{13.601} \approx 15.18$$ Year = 2000 + 15.18 \approx 2015. 5. For hospital care revenue, the model is $$y = 40.897x + 405.3$$ with $x=0$ at 2001. 6. Revenue in 2010 ($x=9$) is: $$y = 40.897 \times 9 + 405.3 = 368.073 + 405.3 = 773.373$$ billion. 7. To find the year when revenue reaches 1000 billion: $$1000 = 40.897x + 405.3$$ $$40.897x = 594.7$$ $$x = \frac{594.7}{40.897} \approx 14.54$$ Year = 2001 + 14.54 \approx 2015. 8. For employment, the model is $$y = -1.8x + 384.6$$ with $x=0$ at 2000. 9. a) Number of employees in 2005 ($x=5$): $$y = -1.8 \times 5 + 384.6 = -9 + 384.6 = 375.6$$ thousand. b) Number of employees in 2010 ($x=10$): $$y = -1.8 \times 10 + 384.6 = -18 + 384.6 = 366.6$$ thousand. Final answers: - Prescription drug sales: 2005 = 201.605 billion, 2010 = 269.61 billion, 340 billion in 2015. - Hospital care revenue: 2010 = 773.373 billion, 1 trillion in 2015. - Employment: 2005 = 375.6 thousand, 2010 = 366.6 thousand.