SOLUTION: The world population at the beginning of 1990 was 5.3 billion. Assume that the population continues to grow at 2% a year, find the function (Qt) that expresses the world populati

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Question 880717: The world population at the beginning of 1990 was 5.3 billion. Assume that the population continues to grow at 2% a year, find the function (Qt) that expresses
the world population in billions as a function of time t (in years) with t=0 corresponding with the beginning of 1990. If the population continues to grow at 2% a year, find the length of time required for the population to double
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula is:
+Q%28t%29+=+5.3%28+1+%2B+.02+%29%5Et+
where +Q%28t%29+ is in billions
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The population has doubled when
+Q%28t%29+=+10.6+ billion
I can then say:
+10.6+=+5.3%28+1+%2B+.02+%29%5Et+
+2+=+1.02%5Et+
+log%282%29+=+t%2Alog%281.02%29+
+t+=+log%282%29+%2F+log%281.02%29+
+t+=+.30103+%2F+.0086+
+t+=+35.003+
The population will double in 35 years
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check:
+Q%2835%29+=+5.3%28+1+%2B+.02+%29%5E35+
+Q%2835%29+=+5.3%2A1.02%5E35+
+Q%2835%29+=+5.3%2A2+
+Q%2835%29+=+10.6+
OK