Chapter 8.4, Problem 63E

Between 1990 and 2013, there was a drop in violent crime and a spike in the prison population m the United States. The bar graph shows the number of violent crimes per 100,000 people and the number of imprisonments per 100,000 people for six selected years from 1990 through 2013.

a. Based on the information in the graph, it appears that there was a year when the number of violent crimes per 100.000 Americans was the same as the number of imprisonments

per 100,000 Americans. According to the graph, between which two years did this occur?

b. The data can be modeled by quadratic and linear functions

$$$ $y=0.6x^2-28x+730$

$$$ $-15x+y=300$

In each function, r represents the number of years after 1990 and y represents the number per 100,000 Americans. Solve a nonlinear system to determine the year described in part (a). Bound to the nearest year. How main violent crimes per 100,000 Americans and how many imprisonments per 100,000 Americans were there in that year?