SOLUTION: You pay off a debt of $550 by paying 19% of the remaining balance each month. Find a formula that gives the remaining debt D after t months. D = ___________ My answer was com

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Question 1042378: You pay off a debt of $550 by paying 19% of the remaining balance each month. Find a formula that gives the remaining debt D after t months.
D = ___________
My answer was completely wrong. I have no idea how to solve this.
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You pay off a debt of $550 by paying 19% of the remaining balance each month. Find a formula that gives the remaining debt D after t months.
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After each payment, you owe 81%.
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D = $550*0.81^t

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe I can do it step by step
If I let +t+=+0+ ( no months have passed )
+D%280%29+=+550+
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+t+=+1+
+D%281%29+=+550+-+.19%2A550+
+D%281%29+=+550%2A%28+1+-+.19+%29+
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+t+=+2+
+D%282%29+=+550%2A%28+1+-+.19+%29+-+.19%2A%28+550%2A%28+1+-+.19+%29+%29+
+D%282%29+=+550%2A%28+1+-+.19+%29%2A%28+1+-+.19+%29+
+D%282%29+=+550%2A%28+1+-+.19+%29%5E2+
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This pattern continues, so the general formula is:
+D%28t%29+=+550%2A%28+1+-+.19+%29%5Et+
+D%28t%29+=+550%2A.81%5Et+
I hope you see this. Each month 19% of the
PREVIOUS months balance gets subtracted.