Download 4.1 Transformations The following table shows the average distance

4.1 Transformations
1. The following table shows the average distance (in millions of miles) of each of the nine planets
(including Pluto) from the sun, and the length of the year (in earth years):
Planet
Distance from Sun
Length of Years
Mercury
36
0.24
Venus
67
0.61
Earth
93
1.00
Mars
142
1.88
Jupiter
484
11.86
Saturn
887
29.46
Uranus
1784
84.07
Neptune
2796
164.82
Pluto
3666
247.68
(a) Is a linear model appropriate between distance from the sun vs length of year? Explain.
(b) Transform the data to make a more appropriate linear model. Is this model an appropriate linear
model between distance from sun vs length of year? Explain.
(c) There has been some debate among astronomers as to whether Pluto is truly a planet or actually a
large member of the Kuiper Belt of comets and other icy bodies. Does your model suggest that Pluto
may not belong in the planet group? Explain.
(d) Scientists did find a new large body, called Quaroar, in orbit the around the sun. Quaroar orbits the
sun every 288 years at a distance of about 4 billion miles. Use your linear model to approximate what
a planet would orbit the sun if 4 billion miles from it (show how you got it). Is this close to the actual?
2. Federal expenditures on social insurance (chiefly social security and Medicare) increased rapidly after 1960.
here are the amounts spent, in millions of dollars:
YEAR
1960
1965
1970
1975
1980
1985
1990
SPENDING 14,307
21,807
45,246
99,715
191,162 310,175 422,257
(a) Is a linear model appropriate for social insurance expenditures on time? Make sure to discuss all 4
points.
(b) Transform the data to make a more appropriate model and discuss this new model.
(c) Use the line to estimate what the expected social insurance outlays for 1988.
(d) The actual amount spent in 1988 was $358,412. Take the log of this amount and add the point 1988
point to your graph in (b). Does it fall close to the line? When President Reagan took office in 1981,
he advocated a policy of slowing growth in spending on social programs. Did the trend of exponential
growth in spending for social insurance change in a major way during the Reagan years, 1981 to 1988?