SOLUTION: Between the start of 2005 and the end of 2009, the number of Facebook users can be modelled by the exponential equation u=0.43x(3.17)^t where u is the number of users in millions

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Between the start of 2005 and the end of 2009, the number of Facebook users can be modelled by the exponential equation u=0.43x(3.17)^t where u is the number of users in millions      Log On


   

Question 1035413: Between the start of 2005 and the end of 2009, the number of Facebook users can be modelled by the exponential equation u=0.43x(3.17)^t where u is the number of users in millions and t is the number of years since the start of 2004 (1<=t,6). So after 1 year (t=1) there are 1.4 million users (to 1 dp)
Find the number of years in which the exponential model predicts that the number of users would first reach 200 million.
I believe I have worked correctly that year 2 = 4.3 and year 3 = 13.7 but I don't know a 'quick' way to reach 200 million
Thank You
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+u+=+.43%2A3.17%5Et+
+200+=+.43%2A3.17%5Et+
%28+2%2F.43+%29%2A10%5E2+=+3.17%5Et+
+4.6512%2A10%5E2+=+3.17%5Et+
Take log base 10 of both sides
+log%28+4.6512+%29+%2B+2+=+t%2Alog%28+3.17+%29+
+.6676+%2B+2+=+t%2A.5011+
+.5011t+=+2.6676+
+t+=+5.3235+
200 million is reached in 5 years
Would that be past 2009 in 2010? I think so.
---------------------------
check:
+u+=+.43%2A3.17%5Et+
+200+=+.43%2A3.17%5E5.3235+
+200%2F.43+=+464.9315+
+465.1163+=+464.9315+
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Error due to rounding off, or I made some
math error, or both