The endpoints of the interval over which distinct vision is possible are called the near point and far point of the eye. With increasing age, these points normally change. The table shows the approximate near points (in inches) for various ages (in years). (Source: Ophthalmology & Physiological Optics)
Age, x
16
32
44
50
60
Near Point, y
3.0
4.7
9.8
19.7
39.4
(a) Find a rational model for the data by taking the reciprocals of the near points to generate the points ( x , 1 / y ) . Use the regression capabilities of a graphing utility to find the least squares regression line for the revised data. The resulting line has the form . Solve for .
(b) Use a graphing utility to plot the data and graph the model.
(c) Do you think the model can be used to predict the near point for a person who is 70 years old? Explain.
