SOLUTION: The purchasing power of A dollars after t years of r% inflation is given by the model P = Ae^-rt. Assume the inflation rate is currently 3.8%. How long will it take for the purchas

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Question 1041927: The purchasing power of A dollars after t years of r% inflation is given by the model P = Ae^-rt. Assume the inflation rate is currently 3.8%. How long will it take for the purchasing power of $1.00 to be worth $0.76? Round the answer to the nearest hundredth.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P+=+A%2Ae%5E%28-r%2At%29+
+A+ = amount in dollars before inflation
+P+ = amount in dollars after inflation
+r+ = % inflation
+t+ = time in years of r% inflation
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+r+=+.038+
+A+=+1+
+P+=+.76+
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+P+=+A%2Ae%5E%28-r%2At%29+
+.76+=+1%2Ae%5E%28-+.038t+%29+
Take the natural log of both sides
+ln%28+.76+%29+=+-.038t+
+-.27444+=-.038t+
+t+=+7.222+
It will take 7.22 yrs
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check:
+.76+=+1%2Ae%5E%28-+.038t+%29+
+.76+=+1%2Ae%5E%28-+.038%2A7.222+%29+
+.76+=+e%5E%28+-.2744+%29+
+.76+=+.76003+
close enough