SOLUTION: Suppose that in any given year, the number of cases of a disease is reduced by 20%. If there are 10000 cases today, how many years will it take to reduce the number of cases to 100

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Suppose that in any given year, the number of cases of a disease is reduced by 20%. If there are 10000 cases today, how many years will it take to reduce the number of cases to 100      Log On


   

Question 779483: Suppose that in any given year, the number of cases of a disease is reduced by 20%. If there are 10000 cases today, how many years will it take to reduce the number of cases to 1000? Be sure to write the exponential equation used.
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
Suppose that in any given year, the number of cases of a disease is reduced by 20%. If there are 10000 cases today, how many years will it take to reduce the number of cases to 1000? Be sure to write the exponential equation used.
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A:
A%28t%29+=+a%5B0%5D%281+-+r%29%5Et
1000+=+10000%281+-+0.2%29%5Et
0.8%5Et+=+0.1
t+=+log%280.8%2C+0.1%29 ≈ 10.31885 years