The following data represent crime rate against individuals (crimes per 1000 households) and their income in the United States in 2006.

Income ……………………………………… Crime Rate

$5000 …………………………………………… 179.4

11,250 …………………………………………… 217.3

20,000 …………………………………………… 195.7

30,000 …………………………………………… 183.1

42,500 …………………………………………… 166.2

62,500 …………………………………………… 166.8

85,000 …………………………………………… 162.0

(a) Using a graphing utility, draw a scatter diagram of the data using income, x, as the independent variable and crime rate, y, as the dependent variable.

(b) Based on the scatter diagram drawn in part (a), decide on a model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between income and crime rate. Be sure to justify your choice of model.

(c) Using a graphing utility, find the model of best fit.

(d) Using a graphing utility, draw the model of best fit on the scatter diagram drawn in part (a).

(e) Use your model to predict the crime rate of a household whose income is $55,000.