Shrinking faster than any other nation's, the projected decline of Japan's population is 17 percent during the next half century.
Shrinking faster than any other nation's, the projected decline of Japan's population is
Shrinking faster than any other nation, Japan's population has a projected decline of
The population of Japan is shrinking faster than that of any other nation and is projected to decline by
The Japanese population is shrinking faster than any other nation, and it has a projected decline at
Japan's population is shrinking faster than that of any other nation, with a projected decline at
The modifier doesn't make sense as a modifier.
The main sentence says that Japan's population IS shrinking. I.e., it's discussing something that is happening at present.
A projected decline is in the future. So, "with a projected decline" can't be used as a modifier, since the future doesn't describe the present.
Note that the correct answer handles the situation by linking two different verbs——in two different tenses——with "and". No modifier.
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