We let x be the amount of money she put in the bank the first year,
Then the second year was 2*x,
and the third year was 2*2*x=4*x,
and the fourth year was 2*2*2*x=8*x.
And the total amount she put in the bank, $450, is the sum of all four years, or $450 = x+(2*x)+(4*x)+(8*x).
This simplifies to $450=15*x.
And therefore, the amount of money she put in the bank the first year was x=$<<30=30>>30.
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