SOLUTION: if a 30000 machine deprecated 1% of its original value each year, find a function f that expresses the machine's value V after t years have elapsed

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Question 550448: if a 30000 machine deprecated 1% of its original value each year, find a function f that expresses the machine's value V after t years have elapsed
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +V%5B0%5D+=+30000+, the initial value
Let +V%5Bt%5D+ = value after +t+ years
given:
+V%5B1%5D+=+V%5B0%5D+-+.01V%5B0%5D+
+V%5B2%5D+=+V%5B0%5D+-+.01%2A%28+V%5B0%5D+-+.01%2AV%5B0%5D+%29+
+V%5B2%5D+=+V%5B0%5D+-+.01V%5B0%5D+%2B+.01%5E2%2AV%5B0%5D+
+V%5B2%5D+=+V%5B1%5D++-+.01%2A%28+V%5B0%5D++-+.01V%5B0%5D+%29+
+V%5B2%5D+=+V%5B1%5D+-+.01V%5B1%5D+
+V%5B2%5D+=+V%5B1%5D%2A%28+1+-+.01+%29+
+V%5B2%5D+=+V%5B0%5D%2A%28+1+-+.01+%29%2A%28+1+-+.01+%29+
+V%5B2%5D+=+V%5B0%5D%2A%28+1+-+.01+%29%5E2+
-----------------------
I can say
+V%5Bt%5D+=+V%5B0%5D%2A%28+1+-+.01+%29%5Et+
+V%5Bt%5D+=+30000%2A.99%5Et+