Solve the problem.Although the number of people arrested for arson has remained fairly constant during the 1990s, the percent of arson arrests that have been juveniles has been on the rise. The data is printed in the table below.
(Source: U.S. Justice Department)Let P represent the percent of arson arrests that are juveniles at t years since 1990. The equation 
models the data well.i) Use the linear model to predict when 75 percent of arson arrests will be juveniles.ii) Use the linear model to estimate the percent of arson arrests that were juveniles in 1985.iii) Find
the t-intercept. What does it mean in terms of arson arrests?iv) What is the slope of the equation P = 1.83t + 44.76? What does the slope represent in terms of arson arrests?v) Find the P-intercept. What does it mean in terms of arson arrests?vi) Find P when t = 10. What does your result mean in terms of the situation?vii) Find t when P = 100. What does your result mean in term of the situation?
What will be an ideal response?
| i) | 2007 |
iii) (-24.46, 0); No juveniles were arrested for arson in 1965.
iv) 1.83; The percent of arson arrests that were juveniles increases by 1.83 each year.
v) (0, 44.76); The percent of arson arrests that were juveniles in 1990 was 44.76%.
vi) 63.06; 63% of arson arrests were juveniles in 2000.
vii) 30.19; All arson arrests will be juveniles in 2020.
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