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The scale factor function (they write it R(t) or a(t)) gives the history of the expansion of the universe, as calculated from observational data. The slope at any moment is the expansion rate at that moment. Which of these best describes how you picture this curve?
1. straightline ramp (constant expansion rate)
2. exponential growth (increasing slope)
3. convex ramp (positive but decreasing slope)
4. silhouette of a woman's breast down to the nipple
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg
the solid dark line is the curve giving the best fit to current astronomical data
1. straightline ramp (constant expansion rate)
2. exponential growth (increasing slope)
3. convex ramp (positive but decreasing slope)
4. silhouette of a woman's breast down to the nipple
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg
the solid dark line is the curve giving the best fit to current astronomical data